A block is attached a horizontal spring ( k = 12.4 N/m) exhibits simple harmonic

Question

A block is attached a horizontal spring (k = 12.4 N/m) exhibits simple harmonic motion on a flat, frictionless table.

The mass is observed to have a maximum displacement of 8.50 cm from its equilibrium position and completes 8 cycles in 10 seconds. At time t = 0, the mass is 1.00 cm to the left of equilibrium and is travelling to the left.

Assume the positive direction is to the right.

a) Find the angular frequency of the block.

b) Find the mass of the block.

d) Find the total energy stored in the block at t = 3.0 s

Explanation / Answer

k = 12.4 N/m
A = 8.5 cm
T = 10/8 = 1.25 s
f = 1/T = 1/1.25
a) w= 2pif = 2*3.14/1.25 = 5.024 Hz
b) w = sqroot(k/m)
5.024 = sqroot(12.4/m)
m = 0.49127g
c) x = 8.5cos(5.024t + phi)
at t = 0
x = -1 cm
-1 = 8.5cos(phi)
phi = 1.6878 rad
x = 8.5cos(5.024t + 1.6878)
d) Total energy at any time = 0.5kA^2 = 0.044795 J

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