Consider a spring hung vertically from the ceiling. (a)[5 pt(s) ]An object is at
ID: 1382068 • Letter: C
Question
Consider a spring hung vertically from the ceiling.
(a)[5 pt(s) ]An object is attached to a k = 300 N m spring. It then undergoes simple harmonic motion with a period of 1 3 seconds. What is the inertia of the object?
(b)[5 pt(s) ]You pull the object in part (a) so that it undergoes simple harmonic motion with an amplitude of 6cm. What is its maximum acceleration and velocity?
(c)[5 pt(s) ]Taking upward to be positive, at what position in the motion do the maximum position, velocity and acceleration occur?
(d)[5 pt(s) ]If we call the time where it is first passing through the equilibrium position on the way up t = 0, write an equation of motion for the oscillation, x(t) =?, identifying the values of all constants that you use.
Explanation / Answer
From the relation
T = 2pi*sqrt(m/K)
1.3 = 2pi*sqrt(m/300)
mass , m = 12.85 kg
b) maximum acceleration = w^2 * A
w = 2pi/T = 6.28/1.3= 4.83 rad/s
A = 6 cm = 0.06
so, a = 4.83^2*0.06 = 1.40 m/s^2
c) maximum position occurs at 6 cm
d) x(t) = Asin(wt+phi)