Problem 19E

A mass on a string of unknown length oscillates as a pendulum with a period of 4.00 s. What is the period if

a. The mass is doubled?

b. The string length is doubled?

c. The string length is halved?

d. The amplitude is halved?

Parts a to d are independent questions, each referring to the initial situation.

Solution 19 E:

Step 1 of 1:-

The oscillation time period is given as,

.

The mass is m.

The length of the string is .

a)

If the mass is doubled, means , then what will be the time period.

We know that,

------------(1)

Where g is the acceleration due to gravity.

The above equation is independent of the mass attached with the string.

So, when the mass is doubled, the time period will remain same as 4 s.

b)

When the string length is doubled,

.

So, the time period will become 5.65 s.

c)

When the string length is halved,

.

So, the time period will become 2.82 s.

d)

When the amplitude is halved, the time period will be invariant. Because it is independent of the amplitude.

But if the angle increases more and we cannot take the approximation of anymore, then this formula will not hold.