Question

Oscillations

Q : The simplest example of simple harmonic motion is the oscillations of a simple pendulum.
a. Derive an expression for the period of oscillation of a simple pendulum.

b. In a simple pendulum made of a metallic wire, what will happen to the period when the temperature
increases? Give a reason.

c. A girl is swinging on a swing in the sitting position. How will the period of swing be affected if she standsup?

​

Answer 1

Answer:

Time period T= time required to complete one oscillation.

At equilibrium T

0

=mg.

For small displacement θ

Restoring force =−mgsinθ

for small θ sinθ≈θ

⇒fe=−mgθ=−mg(

l

x

)

acceleration a=

m

fe

=

l

−g

.x

We know for SHM, a=−w

2

x

⇒ On comparing we get w=

l

g

∴ Time period of oscillation T=

w

2Π

=2Π

g

l

.