Question

The bob of the simple pendulum takes 0.25 seconds to go from one extreme position to its mean position. Calculate the time period of the pendulum

Answer 1

The time period of the pendulum is 1 second.

Explanation:

The time period of the simple pendulum is given by :

$T=2\pi\sqrt{\dfrac{l}{g}}$

l is the length of pendulum

The time period of the pendulum is the time taken by the bob to moves from its one extreme position to another extreme position and coming back to its mean position.

It is given that, the bob of the simple pendulum takes 0.25 seconds to go from one extreme position to its mean position. So, the time period of the pendulum is equal to four times time taken to go from one extreme position to its mean position i.e.

$T=0.25\times 4$

T = 1 second

So, the time period of the pendulum is 1 second. Hence, this is the required solution.

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Answer 2

The time period of pendulum is 1 second.

Given:

Time take by bob to reach mean position from one extreme position = 0.25 s

Explanation:

Time period is time takes by a pendulum to complete one vibration. The distance travelled by the pendulum to reach the two extreme points from its equilibrium position.

Here, time take to reach one extreme point from mean point, time taken to mean point from extreme point, time taken to reach extreme point in other side from mean point and time taken to reach mean point from that point is need to be calculated.

Time period is given by the formula:

T = 4 × (time take to reach one extreme)

On substituting the values, we get,

T = 4 × 0.25

∴ T = 1 second