Question

A simple pendulum executes SHM of period 20 seconds its velocity is 5 metre per second 2 seconds after it has passed through its mean position to determine the amplitude of SHM

Answer 1

Time period, T = 20 s
Velocity of bob, v = 5 m/s
Time, t = 2 s

The displacement of the pendulum can be given as:
y=Acosωt

This implies that the velocity of the bob will be
v=dydt
=−ωAsinωt
v=−2πTAsin(2πTt)   (∵ω=2πT)
5=2π20×A×sin(2π20×2)
=π10×A×sin(π5)
=0.18A
A=50.18
...=27.78 cm

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Answer 2

A simple pendulum executes SHM of period 20 seconds its velocity is 5 metre per second 2 seconds after it has passed through its mean position to determine the amplitude of SHM

Dear Student,

◆ Answer -

● Explanation -

# Given -

T = 20 s

t = 2 s

v = 5 m/s

# Solution -

Angular velocity is given by -

w = 2π/T

w = 2×3.14/20

w = 0.314 rad/s

Formula for speed in SHM is -

v = Awsin(wt)

Substitute values,

5 = A × 0.314 × sin(0.314×2)

5/0.314 = A × sin(0.628)

15.91 = A × 0.5875

A = 15.91 / 0.5875

A = 27.08 m

Hence, amplitude of SHM is 27.08 m.

Thanks dear...