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Chapter 4: Q55P (page 168)

A spring suspended vertically is $18 c m$ long. When you suspend a $30 g$ weight from the spring, at rest, the spring is $22 c m$ long. Next you pull down on the weight so the spring is $23 c m$ long and you release the weight from rest. What is the period of oscillation?

Short Answer

Expert verified

The period of oscillation is $T = 0.4 s$ .

Step by step solution

01

Identification of given data

Given data can be listed below,

Mass, $m = 30 g$
Stretching of spring length $L_{f} = 22 c m$

02

Evaluating spring stiffness

The weight is suspended vertically so that the change of length of the spring is

$鈭� L = L_{f} - L_{i} = 22 - 18 = 4 c m$

Now the spring stretched due to weight vertically suspended its counterbalance or equilibrium the by spring force

$m g = k 鈭� L (30 g) (9.8 m / s^{2}) = k (4 c m) k = 7.35 N / m$

03

The period of oscillation in spring

The period of oscillation of spring is given as

$T = 2 \sqrt{\frac{m}{k}} = 2 蟺 \sqrt{\frac{(30 g) (0.001 k g)}{(7.35 N / m) (1 g)}} = 0.4 s$

Thus, the period of oscillation of spring is $0.4 s$ .

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