Simple Harmonic Motion | MCQs

Explanation

In Simple Harmonic Motion (SHM), instantaneous velocity is maximum when displacement is zero.

This occurs when the phase angle is 90° with respect to displacement (since velocity leads displacement by 90° in SHM).

Explanation

The to and fro movement of a pendulum is called a vibration or oscillation.

It's a repeated back-and-forth motion about a central position.

Explanation

Explanation

In simple harmonic motion (S.H.M), the restoring force is minimum at Mean position. 

The restoring force is directly proportional to the displacement from the mean position.

At the mean position, the displacement is zero, meaning the restoring force is also zero at that point. 

Explanation

A mass attached to a spring oscillates back and forth around an equilibrium position, following Hooke's Law.

This periodic motion with a restoring force proportional to displacement defines simple harmonic motion (SHM).

Explanation

In Simple Harmonic Motion (S.H.M.), frequency is a constant and does not depend on the particle's position (mean or extreme).

• At the mean position, the velocity is maximum, and the acceleration is zero, but the frequency remains constant throughout the motion.

Explanation

Simple harmonic motion (SHM) is also known as oscillatory motion or periodic motion.

It can also be referred to as harmonic oscillation.

It is a system exhibiting SHM that is often called a simple harmonic oscillator. 

Explanation

Total mechanical energy (E) = (1/2) × m × ω^2 × A^2

ω = 2π / T = 2π / 0.20 s = 10π rad/s

m = 40 g = 0.04 kg

A = 2.0 cm = 0.02 m

E = (1/2) × 0.04 kg × (10π rad/s)^2 × (0.02 m)^2

= 8.0 × 10^-3 J

Explanation

To find the frequency, we can use the equation:

v_max = A * ω

where v_max = 31.4 cm/s, A = 5 cm

ω = v_max / A

= 31.4 cm/s / 5 cm

= 6.28 rad/s

Now, ω = 2 * π * f

f = ω / (2 * π)

= 6.28 rad/s / (2 * π)

= 1 Hz

Explanation

if the phase of vibration Θ = π/ z radians, and you are saying that a quarter of the cycle is completed

Then we can equate these two conditions to find the value of z.

In Simple Harmonic Motion (SHM), one complete cycle corresponds to 2π radians. Therefore, if  Θ = π/ z radian represented a quarter of the cycle, then we can write:

 Θ = π/ z = 1/ 4 x 2 π

simplifying 

  π/ z =  π/ 2

 Now, to find the value of z, we can cross-multiply

z = 2

So, when the phase of vibration Θ = π/ z radians and a quarter of the cycle is completed, the value of z is 2.