4. An ideal spring is lying horizontally on a frictionless surface. One end of t

Question

4. An ideal spring is lying horizontally on a frictionless surface. One end of the spring is attached to a wall. The other end is attached to a moveable block that has a mass of 5 kg. The block is pulled so that the spring stretches from its equilibrium position by 0.65 m. Then the block is released (from rest), and as a result the system oscillates with a frequency of 0.40 Hz (that's 0.40 rev/sec). Find... a. the acceleration of the block when the spring is stretched by 0.28 m b. the maximum force magnitude exerted by the spring on the block c. the oscillation frequency of a 2.5 kg block using the same spring and initial displacement.

Explanation / Answer

a)

oscillation frequency of the block is given by :

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

= sqrt(k/5)/(2*pi) <----------- k = spring constant

So, f = 0.4 = sqrt(k/5)/(2*pi)

So, k = 31.6 N/m

So, acceleration, a = k*x = 31.6*0.28 = 8.85 m/s2 <--------- answer

b)

Maximum force, F = k*A

= 31.6*0.65 = 20.54 N <------- answer

c)

oscillation frequency , f = sqrt(31.6/2.5)/(2*pi)

= 0.566 Hz <--------- answer

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