(a) Find the amplitude, frequency, and period of motion for an object vibrating

Question

(a) Find the amplitude, frequency, and period of motion for an object vibrating at the end of a horizontal spring if the equation for its position as a function of time is the following.

Please show all work so i can learn how to do the problem.

Find the amplitude, frequency, and period of motion for an object vibrating at the end of a horizontal spring if the equation for its position as a function of time is the following. Find the maximum magnitude of the velocity and acceleration. What are the position, velocity, and acceleration of the object after 1.50 s has elapsed?

Explanation / Answer

comparing the given equation x= (0.255 m) cos(Pie/8t) with-

x = Acos(2*pi*f*t)....

a)A = 0.255 m

pi/8 = 2*pi*f

=>f = 1/16 = 0.0625 Hz

T = 1/f = 16 sec

b)w = 2*pi*f

Vmax = A(2*pi*f) = 0.1 m/sec

amax = Aw^2 = 0.0393 m/s^2

c)

position x=(0.255 m) cos(Pie/8 * 1.5)=0.212 m

v=dx/dt= -A *w*sin (wt)= - 0.05556 m/sec

a=dv/dt=A *w^2*cos (wt)=(0.0393) cos(Pie/8 * 1.5)= 0.03268 m/s^2

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