A particle undergoes simple harmonic motion. Which of t yti,dw-:bb)d he following can be an expression of a,bd -)iw:ybt dcceleration $a$ in terms of displacement $x$ and a constant value $k$?

  Below are the graphs of the kinetic and potential energies against displacement $s$ for an object exhibiting simple harmonic motion.


Which of the positions marked on the axis represents the location of maximum speed?

  A mass M hangs in equilibrium on a spring. The mass is pulled down 10 $cm$ below the equilibrium position and released. It oscillates vertically about the equilibrium position performing simple harmonic motion.
If it takes 0.5 $s$ after release to return to its equilibrium position, which of the following is true for its first oscillation?

  A mass-spring system y,-fa gl5e,heb3x+p xu4a 0ns has a period of $T_0$​. Another mass-spring system has a mass twice as large with a spring that requires four times as much force to obtain the same extension as the first system.
What is the new period in terms of $T_0$?

  An object on a horizontal spring performs simple harmm5*9r ia.xw ;0 xqylqanhj7l p,rc0i( onic motion. The position of the object as a function of timelr(rlqx97xnc yi0iphw a 5a ;0q,m. *j is given by $x=5\cos (2t).$
Which of the following expressions gives the acceleration of this object as a function of time?

  An object executes simple harmonic motion w u( lv :3nki-b)-6mysoltubc/w56 yt pith an amplitude of $x_0$​. Which graph shows the relationship between the kinetic energy $E_k$​ and the displacement $x$ from the equilibrium position of the object?

  A longitudinal wave is travelling in a medium from left to right. The diagram below is a snapshot of plane wave fronts of showing position of particles $X$ (center of compression) and $Y$ (center of rarefaction) in the medium at t=0 s.


1.Distinguish between a transverse wave and a longitudinal wave.
2.In the graph below, the solid line shows the variation of displacement $s$ of particle X with time, and the dotted line shows the variation of displacement of particle Y with time.

(1)Show that the angular frequency $ω$ of the oscillating particles in the medium is $3.9\,rad\,s^{−1}$.
(2)Calculate the speed of the wave in the medium.v=   $cm\,s^{-1}$
3.(1)State the phase difference between particles X and Y.
(2)Determine the speed of particle Y when t=2.3 s.v=   $mm\,s^{-1}$

  For an object undergoing simple harmonic oscillation, the grap p .ovzzj8js,*b w5d)+(j cqcihs show the variation of two quantities for the objec +()sjjjz c.pz* iqcbo,v85wd t with time t。


Which two quantities could be represented by these graphs?

  For a body executing simple harmonic motion, which statement is not possible?

  A simple pendulum undergoeg ;t0wsxop4xxevyh5y g 3/k-*s simple harmonic motion. The graph shows the variation x/ -xx wehpogk3t50y *ygv4s;of a quantity $y$ with horizontal displacement $x$ from the equilibrium position.


Which of the following quantities could be represented by quantity $y$?
I. The velocity of the pendulum

II. The kinetic energy of the pendulum
III. The potential energy of the pendulum

  A mass-spring system executes simple harmonic motion with *x8llwg;vz9p f +4sjma period T in a vertical plane. What is the period when the oscillating mass is doubled and the system is brought to a planet where the gravitational field s4wvfjz 8p+sg* xml;l9trength at the surface is halved?

  The graph below shows the variation with displacement $x$ of the acceleration $a$ from the equilibrium position of a particle that undergoes simple harmonic motion.


The magnitude of the slope of the graph is directly proportional to

  Two simple pendulums with leng-s r1ljw8(oj kths $16L$ and $9L$ have masses $4M$ and $3M$ respectively. The period of the mass of $4M$ is $T$. What is the period of mass of $3M$?

  A body performs simple harmonic motion (shm). Which of the following could be the speed against the time graph for one period of motion?

  The bob on a conical pendulum is rotated at constant speed such that ia:fg/zmftx .3t describes a horizontal circle of diameter 15 cm. A lamp is placed so that the shadow of the bob projected on a screen describes simple harmonic motion. What is the displacement of the sh f3.gax: /zfmtadow after the bob has traveled a total distance of $30π\,cm$?

  Two identical objects P and Q *qwn9 t80itoo are connected to identical springs. Both P and Q are per0n tot o9q8*iwforming simple harmonic motion (SHM) around equilibrium level O.


The diagram shows positions of P and Q at time $t=0$. Which graph shows how kinetic energy of P and Q vary with time t?

  A spring-mass system executes simple harmonic motion with an amplitude of 20c52t,v:m aztf:lx) tao 0hko7 7evl.num and maximum elastic potential energy of 100J. What is the displacement of theoavnu 7t,. ez:t 2 m7 klv0xtf):haol5 mass when the elastic potential energy of the system is 25J?

  A 2.0 kg object is attached to a spring and vibrates vertically.


The graph below shows the variation of the acceleration of the object with the displacement x.

1.(1)State and explain whether or not the oscillation of the mass is simple harmonic motion.
(2)On the figure above draw an arrow to show the direction of the acceleration of the mass which is displaced by x.
2.(1)Show that the slope of the graph equals to $\frac{-k}{m}$
(2)By using the graph calculate the spring constant, $k$ of the spring.k=   $Nm^{-1}\,kgs^{2}$
3.For the same spring-mass system, show that the acceleration of the object is$10\,cms^{−2}$ when the mass is displaced by 0.12 cm. a≈   $cms^{-2}$

  A particle performs simple harmonic motion with a3 ,v jzpmwcd. b jl)qrqiy.-/ )/mome* frequency of $0.05Hz$ The distance traveled by the particle in one complete oscillation is $16\,cm$ Which of the following graphs shows a correct variation of its position?

  An object with a mass of $m$ is connected to a spring on a frictionless horizontal surface.

The object is displaced by $x$ from its equilibrium point $O$ to point $A$ and executes simple harmonic motion with a period of T. Which of the following are true if the object is displaced by $2x$?

I. The angular frequency of the oscillation will be less.
II. Total energy of the object will be greater.
III. The average speed of the object will not change.

  The graph shows the variation with time $t$ of the displacement $s$ of an object suspended by a spring. At what time is the acceleration in the negative direction at a maximum?

  A mass-spring system rests on a frictionless surface. The mass is pulled to the right and released from point X at $ t=0\,s$.


following correctly shows directions of velocity and acceleration of the mass at $t=10\,s$?

  1.A small ball of mass 4 y5kb54lupyalot5 ;j $m$ is oscillating on a frictionless curved surface.

$x$ is the horizontal displacement from the middle point $O$ of the motion. The shape of the surface is such that the relationship between net force in the horizontal axis and displacement is given by the expression
$F=-m\frac{gx}{r}$

where g is the acceleration of free-fall and r is the radius of the curvature of the surface.
Outline why the ball performs simple harmonic motion.

2.The radius r of the frictionless surface and the mass m of the ball are $10\,cm$ and $20\,g$ respectively.
(1)Show that $ω=\sqrt{\frac{g}{r}}$
(2)Calculate, in $s$, the time taken for the ball to reach point $O$ after being released from the highest point.The time needed for the motion=   s
(3)Draw, on the axes, the graph to show how the kinetic energy of the ball varies with displacement during its motion from the start until it reaches point $O$. Be sure to include the values for the vertical and horizontal intercepts.

  1.Define simple harmonic motion (SHM)

2.An object of mass $5.0\,g$ undergoes simple harmonic motion. The graph shows how displacement $x$ of the object from the equilibrium varies with time $t$.

(1)Calculate, in $rads^{−1}$, the angular frequency of the oscillation.ω=   $rads^{-1}$
(2)Calculate, in N, the maximum net force acting on the object towards equilibrium.Maximum force=   N
(3)Sketch a graph to show how velocity varies with time by using the grid lines below. (There is no need to add values for the y-axis)

3.A metal block connected to a wall with a horizontal spring is oscillating on a rough surface which has a constant coefficient of dynamic friction. Air friction can be ignored.

Deduce whether the metal block executes simple harmonic motion and explain your reasoning.

  A simple pendulum executing simple harmonic motion is released phi49 v gs j):;t/shf-z1fqfgfrom one end and reacs 4 sp vhitg9gffjq1)/-:z;fhhes equilibrium position in $2\,s$. Just after the equilibrium position, the length of the pendulum is reduced to one-fourth of its initial value because of wrapping around a nail.


What is the period of the simple pendulum?

  The graph below shows the variation with displacement of kinetic energy of a 0.20 kg object which is performing simple harmonic motion.


1.Use the graph to determine the total mechanical energy of the object.$E_k​ max$=   mJ
2.On the graph, draw a dotted line that shows the variation with displacement of potential energy of the object.
3.Use conservation of energy to show that the speed of the object is approximately $1.2\,ms^{−1}$ when the displacement is $10\,cm$.v≈   $ms^{-1}$

  An object undergoes simple harmonic motion with a period o+gn9/u2,d cgtdnvz+ of 2s. The amplitude of the motion is 2m and oscillation starts from maximum negative displacement. Which of the following represe nn+ gutgd9odvzc,2+/nts the velocity of the motion?

  A body with maximum rbu31ch vhj5kf)pp141p nh7o8t w;elpotential energy $E_p$​ undergoes simple harmonic motion with amplitude $x_0$​. The body is released from rest from maximum displacement. What is the magnitude of the change in potential energy of the system after the body has moved a distance of $\frac{x_0}{4}$​​?

  An object undergoes simple harmonic motion. The graph shows how accelerah6ybk y c,3kjm2*ticz*;* ar ztion $a$ varies with displacement $x$ from the equilibrium position of the object.


Which of the following gives the displacement of the object when its kinetic and potential energies are equal?

  A metal container filled with sand is stationary on a frictionless surface. It is connected to a wall with a horizontal spring.


The container is pulled in one direction and released. It starts to execute simple harmonic motion with a period of T and a maximum velocity of $v$. Which of the following graphs correctly shows how the velocity would differ if it were released with the same amplitude but with less sand in the container?

  In an experiment to determine the acceleration due to gravity, a student sets uv3j2uj69lpho1 *qmf:3c:si ghi sv(ap a simple pendulum and varies the 6 : q1v2al3mv3h:uijhscjfg o*ps i(9 length of the string by a fixed amount and records the time for 15 oscillations.
Initially, the pendulum starts with a period of $1.0\,s$. The length is then increased by 16%. What will be the approximate percentage increase in the period of the pendulum for the new length?