Question

A simple pendulum is constructed from a bob of mass m = 120 g and a lightweight string of length ℓ = 1.10 m. What are the periods of oscillation for this pendulum in the following situations? (Give your answers to at least two decimal places.)

(a) in a physics lab at sea level
(b) in an elevator accelerating upward at 1.50 m/s²
(c) in an elevator accelerating downward at 1.50 m/s²
(d) in a school bus accelerating horizontally at 1.50 m/s²

Answer 1

time period of a simple pendulum=2*pi*sqrt(L/a)

where L=length of the pendulum=1.1 m

a=effective acceleration of the pendulum

part a:

in a physics lab at sea level, value of g=9.8 m/s^2

then time period=2*pi*sqrt(1.1/9.8)=2.1051 m/s^2

part b:

when elevator is acceleration upwards, effective acceleration =9.8+1.5=11.3 m/s^2

then time period=2*pi*sqrt(1.1/11.3)=1.9604 seconds

part c:

when the elevator is accelerating downwards, then effective acceleration=9.8-1.5=8.3 m/s^2

then time period=2*pi*sqrt(1.1/8.3)=2.2874 seconds

part d:

when it is accelerating horizontally, effective acceleration=sqrt(9.8^2+1.5^2)=9.9141 m/s^2

then time period=2*pi*sqrt(1.1/9.9141)=2.0929 seconds