Question

Shm with frequency f if the mass increased 4 times the frequency will be

Answer 1

We know, time period of a simple harmonic motion is T= 2π√(m/k)

where, 'k' is the spring constant and 'm' is mass of the object.

We know, Time is inversely proportional to frequency.

So, Frequency of a Simple harmonic motion is

f= (1/2π)√(k/m). So we see that frequency is inversely prop. to square root of mass.

Let initial frequency f₁= (1/2π)√(k/m₁)

If mass of the body is increased by 4 times, m₂=4m₁ then frequency

f₂=(1/2π)√(k/m₂)= (1/2π)√(k/4m₁)=(1/2)f₁

Thus, if mass increases by r times, frequency of oscillation will be decreased by half.