Question

An object executing simple harmonic motion has a maximum speed v_max and a maximum acceleration a_max.

(a)  Find the amplitude of this motion. Express your answer in terms of the variables v_max and a_max.

A = __ ?

(b)  Find the period of this motion. Express your answer in terms of the variables v_max and a_max.

T = __ ?

Answer 1

in an SHM

v(max) = A*w ---------(1)

a(max) = w^2*A . --------(2)

w = sqrt( a(max) / A)

v(max) = A* sqrt( a(max) / A)

v(max) = sqrt ( A * a(max))

a) A = v(max)^2 / a(max)

so amplitude is v(max)^2 / a(max)

b) w = sqrt( a(max) / v(max)^2 / a(max))

w = sqrt( a(max)^2 ./ v(max)^2)

w = a(max) / v(max)

w = 2pi/T

2pi/T = a(max)/ v(max)

T = 2pi*v(max) / a(max)