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.
$$\sqrt {\frac{{{k_2}}}{{{k_1}}}} $$
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
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.
$$2\pi \sqrt {\frac{L}{{g\tan \alpha }}} $$
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.
$${T_1} = 2{T_2}$$