A simple harmonic oscillator consisting of an object attached to a horizontal sp

Question

A simple harmonic oscillator consisting of an object attached to a horizontal spring has an amplitude of 3.50 cm and a maximum speed of 28.0 cm/s. The mass of the object is 0.500 kg. a) What is the angular frequency of the oscillation? (3 points) b) What is the spring constant? (2 points) c) What is the object's speed when the displacement is 1.75 cm from equilibrium? (3 points) d) Write a mathematical expression for the position of the object as a function of time assuming that the spring is initially stretched and the object is released from rest. (2 points) nt

Explanation / Answer

given

A = 3.50 cm = 0.0350 m
Vmax = 28 cm/s = 0.28 m/s
m = 0.500 kg

a) let w is the angular frequency of motion.

we know, Vmax = A*w

==> w = Vmax/A

= 0.28/0.035

= 8.00 rad/s

b) we know, w = sqrt(k/m)

w^2 = k/m

==> k = m*w^2

= 0.5*8^2

= 32.0 N/m

c) Apply conservation of energy

(1/2)*m*v^2 + (1/2)*k*x^2 = (1/2)*k*A^2

(1/2)*0.5*v^2 + (1/2)*32*0.0175^2 = (1/2)*32*0.035^2

==> v = 0.242 m/s   or 24.2 cm/s

d) x = A*cos(w*t)

= 0.035*cos(8.00*t)

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