(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 x = (0.235 m) cos( t 8.00 235 4 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. Hz .25 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. s (b) Find the maximum magnitude of the velocity and acceleration 5.9032X max Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. m/s 148.288 X Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. m/s max (c) What are the position, velocity, and acceleration of the object after 1.10 s has elapsed? 208 x Your response is within 10% of the correct value. This may be due to roundoff error, or you = could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. m v 2.737 = The response you submitted has the wrong sign. m/s

Explanation / Answer

given

x= 0.325) cos 1.65 t

when

t = 0.250

x= 0.325) cos 1.65 (0.250)

=0.297 m

(b)

v = dx/dt

=-1.65( 0.325) sin wt

= -1.65 ( 0.325) sin ( 1.65( 0.250)

=-0.214 m/s

(c)

a = dv/dt

= - w^2 A cos wt

= -(1.65)^2 ( 0.325) cos (1.65 ( 0.250)

=-0.810 m/s^2

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