A simple pendulum of length 1 metre has a bob of mass 100 grams.It is displaced through an angle 60 degree and then released.Calculate the speed of the bob when the pendulum passes through the mean position.

To calculate the speed of the bob when the pendulum passes through the mean position, we can use the principles of simple harmonic motion.

Step 1: Determine the period of the pendulum.
The period of a simple pendulum is given by the formula T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

Given:
Length (L) = 1 meter
Acceleration due to gravity (g) = 9.8 m/s^2 (approximate value)

Plugging in the values, we can calculate the period:
T = 2π√(1/9.8)
T ≈ 2π√(0.102)
T ≈ 2π * 0.320
T ≈ 0.640π seconds

Step 2: Calculate the angular frequency.
The angular frequency is given by the formula ω = 2π/T, where ω is the angular frequency and T is the period.

Plugging in the value of the period calculated in step 1, we can calculate the angular frequency:
ω = 2π/0.640π
ω ≈ 3.14/0.640
ω ≈ 4.91 rad/s

Step 3: Calculate the speed at the mean position.
The speed of the bob at the mean position (when the pendulum passes through the middle of its swing) can be found using the formula v = ω * A, where v is the speed, ω is the angular frequency, and A is the amplitude (displacement).

Given:
Amplitude (A) = 60 degrees = 60 * π/180 radians

Plugging in the values, we can calculate the speed at the mean position:
v = (4.91 rad/s) * (60 * π/180 rad)
v ≈ (4.91 * 1/3) m/s

Therefore, the speed of the bob when the pendulum passes through the mean position is approximately 1.637 m/s.