Question

A 0.500 kg mass is attached to a horizontal spring and oscillates such that its position vs. time plot is given below. x Im) 1.0 0.5 .0 2.0 -0.5 (a) What is the period of motion? (b) What is the angular frequency? rad/s (c) What is the spring constant of the spring? N/m (d) What is the fastest speed the mass attains? m/s (e) What is the total mechanical energy of the system?

Answer 1

Here ,

a) from the graph ,

period of motion = 0.60 s

the period of motion is 0.60 s

b) angular frequency = 2pi/T

angular frequency = 2pi/.60

angular frequency = 10.5 rad/s

c) let the spring constant is k

w = sqrt(k/m)

10.5 = sqrt(k/0.50)

solving for k

k = 55.1 N/m

the spring constant is 55.1 N/m

d) let the fastest speed is v

0.5 * 0.50 * v^2 = 0.50 * 55.1 * 0.20^2

solving for v

v = 2.1 m/s

the fastest speed is 2.1 m/s

e) total mechanical energy = 0.50 * 55.1 * 0.20^2

total mechanical energy = 1.1 J