Question

A student wanted to make a pendulum, the time period of which would be one second. He used a string of length L and found that that period was 1/2 seconds. A string of what length must have been used in order to get the desired period?

Answer 1

Question #54634, Physics - Mechanics | Kinematics | Dynamics

A student wanted to make a pendulum, the time period of which would be one second. He used a string of length $L$ and found that that period was 1/2 seconds. A string of what length must have been used in order to get the desired period?

Answer:

The period of a pendulum is defined by the equation:

$$T = 2\pi (L/g)^{0.5}$$

, where $L$ – the length of string and $g$ – the constant which equals $9.18 \, \text{m/s}^2$, and $\pi = 3.14$

For the half-second period, the period is: $T_1 = 2\pi (L_1 / g)^{0.5} = 0.5 \, \text{s}$

For the one second period, the period is: $T_2 = 2\pi (L_2 / g)^{0.5} = 1 \, \text{s}$

Then, $T_2 / T_1 = (L_2 / L_1)^{0.5} = 1 / 0.5 = 2$

$$L_2 / L_1 = 4$$

Thus, the length must be in 4 times longer than that used for 0.5 sec pendulum. If the first string has the length of $L$ then the length to get the desired period is of 4L.

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