⭐ Expected / Important Questions

Oscillations

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).

🏫 CBSEClass 11Physics·19 important questions

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

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

The time period of a seconds pendulum is:

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

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

At what displacement from the mean position is the kinetic energy equal to potential energy in SHM?

What is the time period of a simple pendulum inside a freely falling elevator?

If a spring of spring constant $k$ is cut into two equal halves, the spring constant of each half will be:

Resonance occurs in forced oscillations when the frequency of the external driving force is:

At the mean position ($x = 0$), a body executing SHM has:

In damped harmonic oscillations, the amplitude of oscillation:

The time period of a simple pendulum depends on:

In Simple Harmonic Motion (SHM), the acceleration of a particle is directly proportional to its:

The time period of a simple pendulum in a freely falling lift is:

The phase difference between displacement and acceleration of a particle in SHM is:

What is the approximate length of a second's pendulum on Earth?

If a simple pendulum is taken to Moon where acceleration due to gravity is $g/6$, its time period will increase by a factor of:

Which of the following differential equations correctly represents simple harmonic motion?

A body of mass $1\text{ kg}$ is attached to a spring of spring constant $100\text{ N/m}$. The time period of its oscillation is: