Determine its maximum angular displacement?

[andric_mcneil]

Really Stuck here I've got the period but after that like i said I'm stuck

A simple pendulum having a length of 1.53 m and a mass of 6.74 kg is given an initial speed of 1.36 m/s at its equilibrium position. Assume it undergoes simple harmonic motion.
(a) Determine its period.
2.48 s
(b) Determine its maximum angular displacement.
°

 

[andrevdh]

Use conservation of energy.

 

[ogb p]

The maximum angular displacement of a simple pendulum can be determined using the equation: θmax = A, where A is the amplitude of the motion. In this case, the amplitude can be calculated using the given initial velocity and the length of the pendulum.

First, we need to convert the linear velocity to angular velocity using the formula ω = v/r, where ω is the angular velocity, v is the linear velocity, and r is the length of the pendulum.

ω = 1.36 m/s / 1.53 m = 0.888 rad/s

Next, we can use the formula for the period of a simple pendulum T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity (9.8 m/s²).

T = 2π√(1.53 m / 9.8 m/s²) = 2.48 s

Now, we can use the formula for the amplitude A = θmax = (v/ω)sin(ωt), where t is the time at which the pendulum reaches its maximum displacement.

Since the pendulum starts at its equilibrium position, we can set t = 0.

A = (1.36 m/s / 0.888 rad/s)sin(0) = 0

Therefore, the maximum angular displacement of the pendulum is 0°. This means that the pendulum does not swing past its equilibrium position and only oscillates back and forth within a 0° range.

In conclusion, the maximum angular displacement of the simple pendulum is 0°.