9. A mass of 0.2 kg is attached to a spring of force constant 200 N/m and oscill

Question

9. 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
he equilibrium position (x0 = 0.03 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 x0 = 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 = 1/2 *200 *.03^2 =.09 J intial kinetic energy =0 total mechanical energy = initial potential energy+ intial kinetic energy = .09 joule b) angular frequency = sqrt( K/M) K is spring constant and M is mass. it is independent of intial amplitude .angular frequency doesnot change c) at x = 0 ( mean position ) it has maximum velocity ( potential energy = 0 at x= 0;) d) dv/dt= accleration is maximum at extreme positions

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