Question

A 6.0 kg object attached to a horizontal spring oscillates with an amplitude A = 10 cm and a frequency f = 2.2 Hz.

(a) What is the force constant of the spring?
_____N/m

(b) What is the period of the motion?
_____s

(c) What is the maximum speed of the object?
_____m/s

(d) What is the maximum acceleration of the object?
_____m/s²

Answer 1

Mass of the object = m = 6 kg

Amplitude of the oscillation = A = 10 cm = 0.1 m

Frequency of oscillation = f = 2.2 Hz

Spring constant = k

k = 4²f²m

k = 4²(2.2)²(6)

k = 1146.45 N/m

Angular frequency =

= 2f

= 2(2.2)

= 13.823 rad/s

Time period of motion = T

T = 1/f

T = 1/2.2

T = 0.454 sec

Maximum speed of the object = V

V = A

V = (0.1)(13.823)

V = 1.382 m/s

Maximum acceleration of the object = a

a = A²

a = (0.1)(13.823)²

a = 19.107 m/s²

a) Force constant of the spring = 1146.45 N/m

b) Time period of motion = 0.454 sec

c) Maximum speed of the object = 1.382 m/s

d) Maximum acceleration of the object = 19.107 m/s²