Question

A body executing linear simple harmonic motion has a velocity of $$3\,m/s$$  when its displacement is $$4\,cm$$  and a velocity of $$4\,m/s$$  when its displacement is $$3\,cm.$$  What is the amplitude of oscillation?

A. $$5\,cm$$  
B. $$7.5\,cm$$
C. $$10\,cm$$
D. $$12.5\,cm$$
Answer :   $$5\,cm$$
Solution :
Velocity in $$SHM$$  is given by
$$\eqalign{ & v = \omega \sqrt {{a^2} - {y^2}} \cr & {\text{At}}\,\,y = 4\,cm = 0.04\,m,v = 3\,m/s \cr & \therefore 3 = \omega \sqrt {{a^2} - {{\left( {0.04} \right)}^2}} \,......\left( 1 \right) \cr & {\text{At}}\,\,y = 3\,cm = 0.03\,m,v = 4\,m/s \cr & \therefore 4 = \omega \sqrt {{a^2} - {{\left( {0.03} \right)}^2}} \,......\left( 2 \right) \cr} $$
Dividing (2) by (1),
we get $$a = 0.05 = 5\,cm$$

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. $$\sqrt {\frac{{{k_2}}}{{{k_1}}}} $$
View Answer
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
View Answer
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. $$2\pi \sqrt {\frac{L}{{g\tan \alpha }}} $$
View Answer
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

Practice More Releted MCQ Question on
Simple Harmonic Motion (SHM)

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Oscillation and Mechanical WavesSimple Harmonic Motion (SHM)Waves