Set a mass oscillating on a spring. You should probably adjust the speed of the

Question

Set a mass oscillating on a spring. You should probably adjust the speed of the simulation to 1/16 time. Display an energy bar graph for this mass-spring system and watch it while the mass oscillates. At what point/points in the oscillation is the kinetic energy a maximum? At what point/points is the gravitational potential energy a maximum? At what point/points is the elastic potential energy a maximum?

Hang any mass on any of the springs and get the stopwatch. Set the mass oscillating with a small amplitude and time a reasonable number of oscillations (say 20). Now set it oscillating with a large amplitude and time these oscillations. How does the amplitude of the oscillation affect the frequency

Explanation / Answer

1.It is observed that upon increasing the mass on the spring, the frequency decreases.

2.As the softness of spring is adjusted from soft towards hard, the frequency increases.By changing the softness, we are actually setting the spring constant.By increasing hardness or moving towards the Hard mark we are increasing the spring constant.

3.Dependence of frequency on softness and mass hanged is explained by the formula for frequency

f=(1/2pi)sqrt(k/m)

where, m is the mass hanging and k is a factor dependent upon softness or hardness of the spring.

The formula clearly shows that upon increasing the hanging mass, the frequency will decrease as observed in 1.Also making the spring harder increases the spring constant that increases the frequency which has been observed in 2.

4.The kinetic energy is maximum at the equilibrium position(as seen in the bar graph.).The gravitational potential energy is maximumat the topmost point.The elastic potential energy is maximum at the bottommost point.

5. Setting the load to 250g the initial position 30mm below the pivot the time period is observed to be 0.98 s which gives frequency=1/0.96 Hz.Now the initial position from where the weight is left is 20 mm below the pivot.Thus the amplitude selected this time is greater than the previous one. In this case,again, the time period observed is about 0.96 s giving the same frequency as in the previous case.Thus, it can be concluded that the frequaency of oscillation doesn't depend on the amplitude.

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