Oscillations Expected Questions

Q: Which of the following conditions is essential for a motion to be Simple Harmonic Motion (SHM)?

In Simple Harmonic Motion (SHM), the restoring force or acceleration is directly proportional to the displacement from the mean position and acts in the opposite direction to the displacement ($a = -\omega^2 x$).

Q: The phase difference between displacement and velocity of a particle executing Simple Harmonic Motion is:

If displacement $x = A \sin(\omega t)$, then velocity $v = \frac{dx}{dt} = A\omega \cos(\omega t) = A\omega \sin\left(\omega t + \frac{\pi}{2}\right)$. Thus, velocity leads displacement in phase by $\pi/2$ radians or $90^\circ$.

Q: The time period of a seconds pendulum is:

A seconds pendulum is defined as a pendulum whose time period is exactly 2 seconds. It takes 1 second to move from one extreme to the other.

Q: If the length of a simple pendulum is increased by 4 times, its time period becomes:

The time period of a simple pendulum is $T = 2\pi \sqrt{\frac{l}{g}}$. Since $T \propto \sqrt{l}$, if $l$ becomes $4l$, new time period $T' = \sqrt{4} T = 2T$.

Q: The total mechanical energy of a particle executing Simple Harmonic Motion is directly proportional to:

Total energy in SHM is given by $E = \frac{1}{2} m \omega^2 A^2$. Hence, total energy $E \propto A^2$ (square of the amplitude).

Which of the following conditions is essential for a motion to be Simple Harmonic Motion (SHM)?