A 10 g particle undergoes SHM with an amplitude of 2.0 mm, a maximum acceleratio
ID: 1495279 • Letter: A
Question
A 10 g particle undergoes SHM with an amplitude of 2.0 mm, a maximum acceleration of magnitude 8.0 Times 10^3 m/s. and an unknown phase constant phi. What are the period of the motion, the maximum speed of the particle, and the total mechanical energy of the oscillator? What is the magnitude of the force on the particle when the particle is at its maximum displacement and half its maximum displacement? If the phase angle for a block-spring system in SHM is pi/6 rad and the block's position is given by x = x_m cos(omega t + phi), what is the ratio of the kinetic energy to the potential energy at time t = 0? A block of mass M = 5.4 kg, at rest on a horizontal frictionless table, is attached toExplanation / Answer
the maximum accleration is
a_max = w^2 A
w = sqrt a_max/A
( 2 pi/T) = sqrt a_max/A
T = 2 pi/sqrt a_max/A
= 2 pi/sqrt 8000/0.002
=0.00314 s
(b)
v_max = wA= ( 2pi/T) A
= 2pi/0.00314) ( 0.002)
=4 m/s
(c)
E = 1/2 kA^2 = 1/2 * ( w^2 m) A^2 = 1/2 * ( 2 pi/T)^2 m A^2 = 1/2 * ( 2pi/0.00314)^2 ( 0.010)(0.002)^2 = 0.08 J
(d)
F = mw^2 x
when x = A =
F = 0.010 ( ( 2pi/0.00314)^2 (0.002) = 80 N
when x= A/2
F = 40 N
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