One end of a spring of constant k =100 N/m is attached to a wall.To the other en

Question

One end of a spring of constant k =100 N/m is attached to a wall.To the other end is attached a mass, m = 2.1 kg. The mass isdisplaced 0.15 m from equilibrium and released from rest at t = 0s.
a) Find the period of simple harmonic motion for themass. b)find the angular frequency of simple harmonic motion for themass. c) find the maximum and maximum speeds of the mass in thecourse of its motion. d)find the maximum and minimum acceleration of themass. e)at time t= 1s, find the position, velocity, and accelerationof the mass.
a) Find the period of simple harmonic motion for themass. b)find the angular frequency of simple harmonic motion for themass. c) find the maximum and maximum speeds of the mass in thecourse of its motion. d)find the maximum and minimum acceleration of themass. e)at time t= 1s, find the position, velocity, and accelerationof the mass.

Explanation / Answer

Spring constant k = 100 N / m mass m = 2.1 kg amplitude A = 0.15 m (a). the period of simple harmonic motion for the mass T= 2[ m / k ]                                                                                      = 0.9105 s b)The angular frequency of simple harmonic motion for themass. w = [ k / m ]                                                                                                      = 6.9 rad / s c) maximum speeds of the mass in the course of itsmotion. V = Aw                                                                                             = 1.035 m / s minimum speed = 0 d)minimum acceleration of the mass. a= 0 Maximum accleration of the mass a ' = Aw ^ 2                                                         = 7.142 m / s ^ 2

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