Question

The acceleration of a block attached to a spring is given by a=−(0.324m/s2)cos([2.23rad/s]t). What is the frequency of the block's motion? 0.355 Hz. What is the maximum speed of the block? What is the amplitude of the block's motion?

Answer 1

given

a = -0.324*cos(2.23*t)

from the above equation, w = 2.23 rad/s

f = w/(2*pi)

= 2.23/(2*pi)

= 0.355 Hz

we know,

a_max = 0.324 m/s^2

we know, a_max = A*w^2 ----------(1)

(where A is the amplitude of motion)

v_max = A*w ---------(2)

take equation(2)/equation(1)

v_max/a_max = A*w/(A*w^2)

v_max = a_max/w

= 0.324/2.23

= 0.145 m/s <<<<<<<<<<<<<--------------Answer

v_max = A*w

A = v_max/w

= 0.145/2.23

= 0.0650 m <<<<<<<<<<<<<--------------Answer