Question

Part of a simple harmonic motion is graphed in the figure, where $$y$$ is the displacement from the mean position. The correct equation describing this $$S.H.M.$$  is
Simple Harmonic Motion (SHM) mcq question image

A. $$y = 4\cos \left( {0.6t} \right)$$
B. $$y = 2\sin \left( {\frac{{10}}{3}t - \frac{\pi }{2}} \right)$$  
C. $$y = 4\sin \left( {\frac{{10}}{3}t + \frac{\pi }{2}} \right)$$
D. $$y = 2\cos \left( {\frac{{10}}{3}t + \frac{\pi }{2}} \right)$$
Answer :   $$y = 2\sin \left( {\frac{{10}}{3}t - \frac{\pi }{2}} \right)$$
Solution :
$$\eqalign{ & {\text{From}}\,{\text{the}}\,{\text{figure,}}\,\,\frac{T}{2} = 0.3\pi , \cr & \therefore T = 0.6\,\pi \,\,{\text{and}}\,\,{\phi _0} = - \frac{\pi }{2}. \cr & {\text{Thus}}\,\,y = A\sin \left( {\omega t + {\phi _0}} \right) = 2\sin \left\{ {\frac{{2\pi }}{{0.6\pi }}t + \left( { - \frac{\pi }{2}} \right)} \right\} \cr & = 2\sin \left( {\frac{{10t}}{3} - \frac{\pi }{2}} \right). \cr} $$

Releted MCQ Question on
Oscillation and Mechanical Waves >> Simple Harmonic Motion (SHM)

Releted Question 1

Two bodies $$M$$ and $$N$$ of equal masses are suspended from two separate massless springs of spring constants $${k_1}$$ and $${k_2}$$ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of vibration of $$M$$ to that of $$N$$ is

A. $$\frac{{{k_1}}}{{{k_2}}}$$
B. $$\sqrt {\frac{{{k_1}}}{{{k_2}}}} $$
C. $$\frac{{{k_2}}}{{{k_1}}}$$
D. $$\sqrt {\frac{{{k_2}}}{{{k_1}}}} $$
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Releted Question 2

A particle free to move along the $$x$$-axis has potential energy given by $$U\left( x \right) = k\left[ {1 - \exp \left( { - {x^2}} \right)} \right]$$      for $$ - \infty \leqslant x \leqslant + \infty ,$$    where $$k$$ is a positive constant of appropriate dimensions. Then

A. at points away from the origin, the particle is in unstable equilibrium
B. for any finite nonzero value of $$x,$$ there is a force directed away from the origin
C. if its total mechanical energy is $$\frac{k}{2},$$  it has its minimum kinetic energy at the origin.
D. for small displacements from $$x = 0,$$  the motion is simple harmonic
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Releted Question 3

The period of oscillation of a simple pendulum of length $$L$$ suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination $$\alpha ,$$ is given by

A. $$2\pi \sqrt {\frac{L}{{g\cos \alpha }}} $$
B. $$2\pi \sqrt {\frac{L}{{g\sin \alpha }}} $$
C. $$2\pi \sqrt {\frac{L}{g}} $$
D. $$2\pi \sqrt {\frac{L}{{g\tan \alpha }}} $$
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Releted Question 4

A particle executes simple harmonic motion between $$x = - A$$  and $$x = + A.$$  The time taken for it to go from 0 to $$\frac{A}{2}$$ is $${T_1}$$ and to go from $$\frac{A}{2}$$ to $$A$$ is $${T_2.}$$ Then

A. $${T_1} < {T_2}$$
B. $${T_1} > {T_2}$$
C. $${T_1} = {T_2}$$
D. $${T_1} = 2{T_2}$$
View Answer

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Simple Harmonic Motion (SHM)

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