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

The period of motion of new mass T = 0.637 sec

Step-by-step 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 = (F)/(x)`

`k = (0.08829)/(0.035)`

k = 2.522
`(N)/(m)`

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

Now the period of motion is given by

`T = 2 \pi \sqrt{(m)/(k) }`

`T = 2 \pi \sqrt{(0.026)/(2.522) }`

T = 0.637 sec

This is the period of motion of new mass.