Question

A simple pendulum has a mass of 0.150 kg and a length of 4.00 m. It is displaced through an angle of 7.0° and then released. Using the analysis model of a particle in simple harmonic motion, calculate the following. (Give your answer to the thousandths place.)

(a) What is the maximum speed of the bob?
m/s

(b) What is the maximum angular acceleration of the bob?
rad/s²

(c) What is the maximum restoring force of the bob?
N

(d) Solve parts below using other analysis models. (Hint: you may need to use separate analysis models for each part.)

1. maximum speed	m/s
2. maximum angular acceleration	rad/s2
3. maximum restoring force	N

(e) Compare the answers.

Answer 1

mass, m = 0.15 kg

length of the pendulum, L = 4 m

angle, ? = 7^o

sin 7^o = A / L

? amplitude, A = L*sin 7^o

                        = 0.49 m

time period of the simple pendulum, T = 2? ?[ L / g] = 2? ?[ 4 / 9.81] = 4.012 s

( a) maximum speed = A ?

where ? =angular frequency = 2? / T = 2? / 4.012 = 1.6 rad/s

maximum speed = A ? = 0.49*1.6 = 0.77 m/s

( b ) maximum angular acceleration = A ?² = 0.49*1.6² = 1.23 rad/s²

( c ) maximum restoring force F = mA ?² = 0.15*1.23 = 0.18 N