Question

A rubber pad acts as an elastic spring. When a mass of 200 g is placed on it, a compression of 2.0 cm is produced. The spring-mass system begins to oscillate when the mass is gently tapped downwards. Calculate the frequency of oscillation.

Answer 1

The frequency of oscillation is 3.55 Hz.

Explanation:

Given that,

Mass, m = 200 g = 0.2 kg

Compression in the spring, x = 2 cm = 0.02 m

The spring-mass system begins to oscillate when the mass is gently tapped downwards. The force of gravity is balanced by the force in spring. So,

$mg=kx$

k is the spring constant

$k=\dfrac{mg}{x}\\\\k=\dfrac{0.2\times 10}{0.02}\\\\k=100\ N/m$

The frequency of oscillation is given by :

$f=\dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}} \\\\f=\dfrac{1}{2\pi}\sqrt{\dfrac{100}{0.2}} \\\\f=3.55\ Hz$

So, the frequency of oscillation is 3.55 Hz.

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