Question

A simple pendulum hangs in equilibrium. A frustrated student walks up to it and kicks the bob so

that it swings with a period of 3.5 co and has a maximum velocity of 0.75 m/. What is the length
of the pendulum?

Answer 1

To calculate the length of a simple pendulum given its period and maximum velocity, we use the formula for the period T = 2π√(L/g) and rearrange it to solve for length, L = (T2g)/(4π²). Plugging in the period of 3.5 seconds results in an approximate pendulum length of 3.05 meters.

Step-by-step explanation:

The question involves calculating the length of a simple pendulum based on its period and maximum velocity. To find the length of the pendulum (L), we can use the formula for the period of a simple pendulum, which is T = 2π√(L/g), where T is the period and g is the acceleration due to gravity (assumed to be 9.81 m/s2 on Earth).

First, we rearrange this formula to solve for L:

• L = (T2g)/(4π²).

Next, we can plug in the given values:

• T = 3.5 s.
• g = 9.81 m/s2.

So, we calculate L as follows:

• L = (3.52 × 9.81)/(4 × π²).
• L ≈ (12.25 × 9.81)/(39.4784).
• L ≈ 120.3075/39.4784.
• L ≈ 3.05 m.

Therefore, the length of the pendulum is approximately 3.05 meters.