13) A mass of 0.2 kg is attached to a spring of force constant 200 N/m and oscil

Question

13) A mass of 0.2 kg is attached to a spring of force constant 200 N/m and oscillates on a frictionless horizontal surface. It is initially released from rest at a point 3.0 cm away from the equilibrium position (i.e. x0 = 3.0 m).
a) What is the initial potential energy, initial kinetic energy and the total mechanical energy?
b) What is the angular frequency of the oscillation? (Does it change if it is released at x = 5.0 cm ?)
c) Where does the mass have the maximum speed?
d) Where does the mass have the maximum acceleration?

Explanation / Answer

a)Initial potential energy=0.5kx2=0.09J

Initial KE=0

Total mechanical energy=0.09J

b)=2*sqrt(k/m)=198.7 rad/s

No it does not depend on displacement.

c)The mass has maximum speed at the unstretched position.x=0

d)The mass has maximum acceleration at the extreme position x=3cm

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