Question

A spring suspended vertically is 11.9 cm long. When you suspend a 37 g weight from the spring, at rest, the spring is 21.5 cm long. Next you pull down on the weight so the spring is 25.2 cm long and you release the weight from rest. What is the period of oscillation?

Answer 1

Answer:

Time period of oscillations is 0.62 s

Explanation:

Due to suspension of weight the change in the length of the spring is given as

$\Delta L = L_f - L_i$

$\Delta L = 21.5 - 11.9 = 9.6 cm$

now we know that spring is stretched due to its weight so at equilibrium the force due to weight is counter balanced by the spring force

$mg = kx$

$0.037 (9.81) = k(0.096)$

$k = 3.78 N/m$

Now the period of oscillation of spring is given as

$T = 2\pi \sqrt{\frac{m}{k}}$

Now plug in all values in it

$T = 2\pi \sqrt{\frac{0.037}{3.78}}$

$T = 0.62 s$