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