A 7 kg mass is connected to a spring (k = 800 N/m) platform which undergoes simp

Question

A 7 kg mass is connected to a spring (k = 800 N/m) platform which undergoes simple harmonic motion in the vertical direction. The amplitude of the oscillation is 5 cm. At t=0 the box is 5 cm above the equilibrium position.
(a) What is the period of oscillation?
s

(b) What is the angular frequency of the box?
rad/s

(c) What is the velocity of the box at the equilibrium position?
m/s

(d) What is the total energy of the 7 kg block?
J

(e) What is acceleration (magnitude and direction) of the box after 5 s (assume mass is at +A at t = 0 s.)?
m/s^2

Explanation / Answer

a) T = 2/ = 2*3.142/(k/m) = 2*3.142/(800/7) = 0.587s

b) = (k/m) = 10.69rad/s

c) v = Asint = 0.05*10.69*sin(10.69*0.587/4) = 0.534m/s

d) E = 0.5kA^2 = 0.5*800*0.05^2 = 1J

e) a = -A^2cost = -0.05*(800/7)*cos(10.69*5) = 5.709m/s^2

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