Question

A mass on a string of unknown length oscillates as a pendulum with a period of 3.5s. Parts a to d are independent questions, each referring to the initial situation. What is the period if:

Part A: the mass is doubled? (s)
Part B: the string length is doubled? (s)
Part C: the string length is halved? (s)
Part D: the amplitude is doubled? (s)

Answer 1

Concepts and reason

The concept used to solve this problem is time period of a simple pendulum.

The time period of oscillation depends on the length of the pendulum and acceleration due to gravity.

Time period of the pendulum is the time required to complete one oscillation.

Fundamentals

Expression for the time period of the pendulum is,

Here, is the period of the pendulum, is length of pendulum, and is acceleration due to gravity.

(A)

Expression for the time period of the pendulum is,

Here, the time period is independent of the mass of the pendulum. Hence the mass has no effect on the period of the pendulum.

Therefore, the period of the pendulum when mass is doubled is .

(B)

Expression for the time period of the pendulum is,

Here the string length is doubled.

Substitute for .

Substitute, for .

Therefore, the period of the pendulum when string length is doubled is .

(C)

Expression for the time period of the pendulum is,

Here the string length is halved.

Substitute for .

$T=21,172 $

Substitute for .

Therefore, the period of the pendulum when string length is halved is .

(D)

Expression for the time period of the pendulum is,

Here, the time period is independent of the amplitude of the pendulum.

Hence the amplitude has no effect on the pendulum.

Therefore, the period of the pendulum when amplitude doubled is .

Ans: Part A

The period of the pendulum when mass is doubled is .

Part B

The period of the pendulum when string length is doubled is .

Part C

The period of the pendulum when string length is halved is .

Part D

The period of the pendulum when amplitude doubled is .