4. -/9 points SerPSET9 15.P.028 My Notes Ask Your Teacher A 3.10-kg object is at

Question

4. -/9 points SerPSET9 15.P.028 My Notes Ask Your Teacher A 3.10-kg object is attached to a spring and placed on frictionless, horizontal surface. A horizontal force of 23.0 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 (b) 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

Explanation / Answer

A.

we know that

F = kx

k = spring constant = F/x

k = 23/0.2 = 115 N/m

B,

w = sqrt (k/m)

w = sqrt (115/3.1) = 6.09 rad/sec

w = 2*pi*f

f = 6.09/(2*pi) = 0.969 Hz

C.

Vmax = A*w

Vmax = 0.2*6.09 = 1.218 m/sec

D.

max speed will occur when kinetic energy is maximum, which will be max when potential energy is zero.

Now potential energy of spring is zero at its natural state, So max speed will be at

x = 0 m

E.

a)max = A*w^2

a)max = 0.2*6.09^2 = 7.42 m/sec^2

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