Question

As an aid in working this problem, consult Concept Simulation 10.3. A block of mass m = 0.815 kg is fastened to an unstrained horizontal spring whose spring constant is k = 87.0 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

Answer 1

a)
Given that mass(m) = 0.815 kg
Spring constant(k) = 87.0 N/m
Displacement(x) = 0.120m
Now formula for calculating the value of the force is
            F = kx
               = (87.0 N/m)(0.120m) = 10.44 N

b)
We know the formula of the angular frequency is
             
= sqrt(87/0.815)
                  = 10.33 rad/s
c)
Now formula for calculating the value of the max speed is
         v_max = A?
                  = (0.120m)( 10.33rad/s)

= 1.24 m/s
d)
Formula for calculating the value of the max acceleration is
          a_max = A?²
                   = (0.120m)( 10.33 rad/s)²

= 12.8 m/s2