A mass is attached to the end of a spring and set into oscillation on a horizont

Question

A mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a stretched position of

x = +0.150 m.

The mass of the block is

m = 0.727 kg,

the force constant of the spring is

k = 69.3 N/m.

Determine the following.

(a) force component that the spring exerts on the block just before the block is released (Indicate the direction with the sign of your answer.)

What does Hooke's law tell us about the force exerted by a spring? N

(b) angular frequency ? of the resulting oscillatory motion
rad/s

(c) maximum speed of the oscillating mass
m/s

(d) magnitude of the maximum acceleration of the oscillating mass
m/s2

Explanation / Answer

#a)

F = -K*x = -69.3*0.15 = 10.395 N <---------answer

#b)

w = sqrt(k/m)

w = sqrt(69.3/0.727) = 9.76 rad/s <------answer

#c) KE max = PEmax

0.5*M*Vmax^2 = 0.5*K*A^2

m*Vmax^2 = m*w^2*A^2

Vmax = A*w = 0.15*9.76 = 1.464 m/s

#d) Fmax = K*A = m*a

m*w^2*A = m*a

a = w^2*A = 9.76*9.76*0.15 = 14.28864 m/s^2

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