As an aid in working this problem, consult Concept Simulation 10.3. A block of m

Question

As an aid in working this problem, consult Concept Simulation 10.3. A block of mass m = 0.880 kg is fastened to an unstrained horizontal spring whose spring constant is k = 72.0 N/m. The block is given a displacement of +0.120 m, where the + sign indicates that the displacement is along the +x axis, and then released from rest.

(a) What is the force (magnitude and direction) that the spring exerts on the block just before the block is released? N

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

(c) What is the maximum speed of the block? m/s

(d) Determine the magnitude of the maximum acceleration of the block. m/s2

Explanation / Answer

(a) By F = -kx
=>F = - 72 x 0.120 = -8.64 N [-ve indicating the force is towards origin]

(b) By T = 2 x pi x sqrt[m/k]
=>T = 2 x 3.14 x sqrt[0.88/72]
=>T = 0.694 sec
=>omega = (2 x pi)/T = 6.28/0.694 = 9.05 rad/sec

(c) By the law of energy conservation:-
=> KE(max) of block = PE(max) of the spring
=>1/2 x mv^2 = 1/2kx^2
=>v = sqrt[kx^2/m]
=>v = sqrt[{72 x (0.12)^2}/0.88]
=>v = 1.09 m/s

(d) By F = ma
=>a(max) = F(max)/m = 8.64/0.88 = 9.82 m/s^2

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