Question

A mass on a string of unknown length oscillates as a pendulum with a period of 1.8 s. What is the period in the following situations? (Parts (a) to (d) are independent questions, each referring to the initial situation.)(a) The mass is doubled?(b) The string length is doubled?(c) The string length is halved?(d) The amplitude is doubled?

Answer 1

Using

Period ( P) is given as

P~√(L/g).

a) since mass has no effect on the period of a pendulum. So, the period will remain 1.8seconds

b) using the formula above ,period varies with the square root of the length. Thus , when the length doubles, the period is multiplied by √2. So, the period is 1.8s*√2 = 2.54s

c) in this case, the period is multiplied by √(1/2).

1.8√(1/2)=1.27s.

d) amplitude of the pendulum doesn't affect the period (unless itsvery high, so, the period is still 1.8s