Answer the following questions. (Assume g = 9.80 m/s^2.) A massless spring havin

Question

Answer the following questions. (Assume g = 9.80 m/s^2.) A massless spring having a spring constant k = 8.75 N/m is hung vertically. If the spring is displaced 0.150 m from its equilibrium position, what is the force that the spring exerts?__ A 400-g mass is suspended from this spring. What is the displacement of the end of the spring due to the weight of the mass?__ Suppose this mass is allowed to oscillate on the spring. What is the period of the oscillation? What is the frequency of the oscillation?__ A 0.100-kg mass suspended vertically on a spring takes 10.94 s to undergo 20 oscillations. What is the spring constant of the spring?__

Explanation / Answer

a)

Force , F = k*x

= 8.75*0.15

= 1.31 N

b)

displacement, x = F/k

= mg/k

= 0.4*9.8/8.75 = 0.448 m

c)

period, T = 2*pi*sqrt(m/k)

= 2*pi*sqrt(0.4/8.75)

= 1.34 s

d)

frequency, f = 1/T = 0.746 Hz

e)

T = 10.94/20 = 0.547 s

Also, T = 2*pi*sqrt(m/k)

So, 0.547 = 2*pi*sqrt(0.1/k)

So, k = 13.2 N/m

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