Question

A spring stretches 3.5 cm when a 9 g object is hung from it. The object is replaced with a block of mass 26 g which oscillates in simple harmonic motion. Calculate the period of motion. The acceleration of gravity is 9.8 m/s 2.

Answer 1

Answer:

The period of motion  of new mass T = 0.637 sec

Explanation:

Given data

Mass of object (m) = 9 gm = 0.009 kg

Δx = 3.5 cm = 0.035 m

We know that spring force is given by

F = m g

F = 0.009 × 9.81 = 0.08829 N

Spring constant

$k = \frac{F}{x}$

$k = \frac{0.08829}{0.035}$

k = 2.522 $\frac{N}{m}$

New mass$(m_1)$ = 26 gm = 0.026 kg

Now the period of motion is given by

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

$T = 2 \pi \sqrt{\frac{0.026}{2.522} }$

T = 0.637 sec

This is the period of motion  of new mass.