A 20 g particle undergoes SHM with an amplitude of 2.0 mm and a maximum accelera

Question

A 20 g particle undergoes SHM with an amplitude of 2.0 mm and a maximum acceleration of magnitude 8.0 103 m/s2, and an unknown phase constant ?.

(a) What is the period of the motion?

(b) What is the maximum speed of the particle?

(c) What is the total mechanical energy of the oscillator?

(d) What is the magnitude of the force on the particle when the particle is at its maximum displacement?

(e) What is this force when the particle is at half its maximum displacement?

Thank you so much for the help!

Explanation / Answer

Mass particle m = 10 g
                         = 0.01 kg
Amplitude A = 2.0 mm
                    = 2 x 10 -3 m
Maximum acceleration a = 2.0 x 10 3 m/s 2
We know a = A 2
From this angular frequency = [ a/A]
                                              = 1000 rad / s
(a) The period of the motion T = 2 /
                                               = 6.283 x 10 -3 s
(b) The maximum speed of the particle V = A
                                                               = 2 m / s
(c) The total mechanical energy of the oscillator E = ( 1/ 2) mV 2
                                                                           = 0.02 J
(d) The magnitude of the force on the particle when the particle is at its maximum displacement
   F = kA
Where k = force constant
                = m 2
                = 10000 N / m
So, F = 20 N
(e) Force when the particle is at half its maximum displacement F ' = kx
Where x = displacment
               = A/ 2
So, F ' = 10 N

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