a .20 kg block is attatched to a horizontal spring of constant k=200 N/m is plac

Question

a .20 kg block is attatched to a horizontal spring of constant k=200 N/m is placed on a horizontal frictionless surface. the block is then pulled to the right so that the spring stretches a distance of .10 m. the block os released at time t=0s and undergoes simple harmonic motion.

a. what is thrle amplitude for thr block?

b. what is the frequency of the motion

c. what is maximum velocity of block?

d. what is maximum acceleration of block?

e. what is total mechanical energy of system ay any instant?

f. what is speed of block each time the spring is stretched 5.0 cm?

g. what is acceleration of the block each time spring is stretched 5.0cm?

Explanation / Answer

A.

As given,

Amplitude = xmax = 10 m   [ANSWER]

***************

B.

As

f = (1/2pi)sqrt(k/m)

Then

f = 0.503 Hz   [ANSWER]

***************

Note that

vmax = xmax (2 pi f)

Thus,

vmax = 31.6 m/s   [ANSWER]

*****************

Note that

amax = xmax (2 pi f)^2

Thus,

amax = 100 m/s^2   [ANSWER, PART D]

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