Answers are at the bottom of question...just need to know how to show all the wo

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Answers are at the bottom of question...just need to know how to show all the work!

A block whose mass m is 680 g is fastened to a spring whose spring constant k is 65 N/m (See figure below). The block is pulled a distance x = 11 cm from its equilibrium position at x = 0.0 on a frictionless surface and released from rest at t = 0.0.
a) What are the angular frequency, the frequency, the amplitude, and the period of the resulting motion?
b) What is the maximum speed of the oscillating block, and where is the block when it occurs?
c) What is the magnitude of the maximum acceleration of the block? d) What is the displacement function x(t) for the spring-block system?

Answer: a) angular freq =9.8 rad/s; frequency = 1.6 Hz, Period = 0.64 s b) 1.1 m/s, c) 11 m/s2 d) write it in x(t) = Acos?t format

Explanation / Answer

a)the stored potential energy of the spring=0.5kx2 =0.5m0.5*65*11*11*10-4 =3932.5J

=k/m=65/0.68=9.77rad/s

   f=/2=9.77/(2*3.14)=1.55Hz

T=1/f=1/1.55=0.64s

amplitude A=11cm

b)maximum speed is at its mean position

v=x=9.77*11*10-2 =1.07m/s

c)maximum acceleration a=-2 x=-9.77*9.77*11*10-2 =-10.49m/s2

-ve sign indicates tht acceleration is opposite in direction with displacement

d)X(t)=Acos(t-kx)=11scos(9.77t-65x)

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