Question

A plastic ball attached to a spring moves in simple harmonic motion. The amplitude of the ball's motion is 11.5 cm, and the spring constant is 6.00 N/m. When the ball is halfway between its equilibrium position and its maximum displacement from equilibrium, its speed is 22.7 cm/s.

What is the mass of the ball (in kg)?

Answer-    kg

What is the period of oscillation (in s)?

Answer- s

What is the maximum acceleration of the ball? (Enter the magnitude in m/s².)

Answer-    m/s^2

Answer 1

Solution) X = 11.5 cm = 0.115 m

K = 6 N/m

V = 22.7 cm/s = 0.227 m/s

Mass of the ball , m = ?

(1/2)(K)(X^2) = (1/2)(K)(X/2)^2 + (1/2)(m)(V^2)

(6)(0.115^2) = (6)(0.115/2)^2 + (m)(0.227^2)

(6)(0.115^2) - (6)(0.115/2)^2 = (m)(0.227^2)

0.0793 - 0.0198 = (m)(0.227^2)

0.0595 = (0.0515)(m)

m = (0.0595)/(0.0515)

m = 1.15 kg

Period , T = ?

T = 2(pi)(m/K)^(1/2)

T = 2(pi)(1.15/6)^(1/2)

T = 2.75 s

Maximum acceleration , a = ?

a = (w^2)(X)

w = (2(pi))/(T)

w = (2(pi))/(2.75)

w = 2.28 rad/s

a = (2.28^2)(0.115)

a = 0.59

Approximately a = 0.6 m/s^2