A 3.1 kg block is attached to a horizontal spring and undergoes simple harmonic

Question

                    A 3.1 kg block is attached to a horizontal spring and undergoes simple harmonic motion on a frictionless surface according to the graph shown above.                 

                                1) What is maximum velocity of the box?                             

                                vmax = _____________________ m/sec                             

                    

2) What is the mechanical energy of the box?                 

                    A = ______________ J

A 3.1 kg block is attached to a horizontal spring and undergoes simple harmonic motion on a frictionless surface according to the graph shown above. What is maximum velocity of the box? What is the mechanical energy of the box?

Explanation / Answer

Here

w = angular frequency = pi4 rad/sec

This is because it travel pi/2 in 2sec

o in 1sec it is pi/4

A = Maximum Amplitude = 2 cm = 0.02 m

vmax = wA

= 0.02*pi/4

= 0.0157 m/sec

mechanical energy of the box = 0.5*m*vmax^2

= 0.5*3.1*0.0157^2

= 0.000382 J

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