Hooke S Law

The time period of SHM is given by:

$T%3D2%5Cpi%5Csqrt%7B%5Cfrac%7Bm%7D%7Bk%7D%7D$

Initially, $T%3D1$ s:

$1%3D2%5Cpi%5Csqrt%7B%5Cfrac%7Bm%7D%7Bk%7D%7D$

Squaring both sides:

$%5Cfrac%7Bm%7D%7Bk%7D%3D%5Cfrac%7B1%7D%7B4%5Cpi%5E%7B2%7D%7D$ ……………(1)

After increasing the mass by 3 kg, the period becomes 2 s:

$2%3D2%5Cpi%5Csqrt%7B%5Cfrac%7Bm%2B3%7D%7Bk%7D%7D$

Squaring both sides:

$%5Cfrac%7Bm%2B3%7D%7Bk%7D%3D%5Cfrac%7B4%7D%7B4%5Cpi%5E%7B2%7D%7D%3D%5Cfrac%7B1%7D%7B%5Cpi%5E%7B2%7D%7D$ ………………(2)

Dividing equation (2) by equation (1):

$%5Cfrac%7Bm%2B3%7D%7Bm%7D%3D4$

Simplify:

$m%2B3%3D4m$

$3m%3D3%20%5CRightarrow%20m%3D1%20%5Ctext%7B%20kg%7D$

Thus, the value of m is 1 kg.

Chapter Questions
1 MCQs