Question

1. A body executes 40 oscillations per minute. Its
maximum speed is 36 cm s. !. Calculate the amplitude
of oscillation
[Kerala 2001] (Ans. 3.82 cm]​

Answer 1

Answer:

The amplitude of oscillation is 8.59 cm

Step-by-step explanation:

Given :

• A body executes 40 oscillations per minute.
• Its  maximum speed is 36 cm s⁻¹

To find :

the amplitude  of oscillation

Solution :

•  Maximum speed is given by,

 v = Aω

where

A denotes the amplitude

ω denotes the angular velocity.

• Angular velocity is given by,

ω = 2πn

where

n denotes frequency.

So, v = A (2πn)

 

we have to find the frequency.

The frequency is the number of oscillations per second.

The body executes 40 oscillations per minute.

In one second, the body executes 40/60 = 2/3 oscillations.

∴ frequency, n = 2/3

Substitute,

$\sf 36 cm \ s^{-1} =A \times 2 \times \dfrac{22}{7} \times \dfrac{2}{3} \\\\ \sf 36=A \times \dfrac{88}{21} \\\\ \sf 36=A \times 4.19 \\\\ \sf A=\dfrac{36}{4.19} \\\\ \sf A=8.59 \ cm$

Therefore, the amplitude of oscillation is 8.59 cm