Question

A 1.30-kg object is attached to a spring and placed on frictionless, horizontal surface. A horizontal force of 21.0 N is required to hold the object at rest when it is pulled 0.200m from its equilibrium position......

Would you write out the intermediate steps, too, please?

A 1.30-kg object is attached to a spring and placed on frictionless, horizontal surface. A horizontal force of 21.0 N is required to hold the object at rest when it is pulled 0.200 m from its equilibrium position (the origin of the x axis). The object is now released from rest from this stretched position, and it subsequently undergoes simple harmonic oscillations. (a) Find the force constant of the spring N/m Find the frequency of the oscillations Hz (c) Find the maximum speed of the object. m/s (d) Where does this maximum speed occur? (e) Find the maximum acceleration of the object. m/s2 (f) Where does the maximum acceleration occur? (9) Find the total energy of the oscillating system. Find the speed of the object when its position is equal to one-third of the maximum value. m/s (I) Find the magnitude of the acceleration of the object when its position is equal to one-third of the maximum value. m/s

Answer 1

"F = -R x = 21 n R = 210/1^2 = 105 N/m frequency will be given by n = 1/2 pi squareroot k/m = 1/2 pi squareroot 1 - 105/1 - 1.3 = 1.43 H_z max^m speed V = w x = 2 pi n x 2 V = 1.7974 m/sec x_0 = plusminus 20 at x = x_0 according to above figure from x = x_0 = equilibrium max^n accl^n