If a simple pendulum oscillates with an amplitude of 50 mm and time period of 2 sec, then its maximum velocity is

• A. 0.10 m/s
• B. 0.16 m/s
• C. 0.25 m/s
• D. 0.5 m/s

To find the maximum velocity of a simple pendulum, we can use the formula:

Maximum Velocity Formula

The maximum velocity (v_max) is given by:

v_max = A * ω

where:

• A = amplitude (in meters)
• ω = angular frequency (in radians per second)

Calculating Angular Frequency

Angular frequency (ω) can be calculated using the time period (T):

ω = 2π / T

Given that the time period T is 2 seconds:

ω = 2π / 2 = π rad/s

Amplitude Conversion

The amplitude is given as 50 mm, which is:

A = 50 mm = 0.05 m

Finding Maximum Velocity

Now, substituting the values into the maximum velocity formula:

v_max = 0.05 m * π rad/s

Calculating this gives:

v_max ≈ 0.05 * 3.14 ≈ 0.157 m/s

Final Answer

Rounding this value, the maximum velocity is approximately 0.16 m/s. Therefore, the correct answer is:

B. 0.16 m/s