Impulse on a pendulum, to maintain amplitude

In summary, to calculate the magnitude of impulse needed to maintain the pendulum's amplitude, you must consider the energy of the system at different points in its cycle and use the difference in energy to calculate the impulse required.
  • #1
indie452
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Hi I am doing some past exam questions for revision and have got stuck on part d) of the attached question.

It is asking, if an impulse is applied to a pendulum, what magnitude of impulse is needed to maintain the pendulums ampiltude.

If it helps the ratio of amplitudes from 2 successive cycles I found to be = exp(-bT/2m), where T=period= 2pi/w


I think w = (velocity immediately after)/(dist. from pivot to impulse) = 10 rad/s
but then i don't know where to go from here.

any help to get started is appreciated
Thanks
 

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  • #2
!To calculate the magnitude of impulse required to maintain the pendulum's amplitude, you need to consider the energy of the system. When an impulse is applied, it adds energy to the system, which will be dissipated by the damping force over time. The total energy of the system (kinetic + potential) must remain constant for the pendulum to maintain its amplitude.To calculate the magnitude of the impulse, you need to calculate the energy of the system at different points in the cycle. For instance, when the pendulum is at its maximum displacement, the kinetic energy is zero and the potential energy is maximum. At this point, calculate the total energy and then calculate the total energy at the other extreme displacement (when the velocity is maximum). You can then use the difference in energy between these two points to calculate the magnitude of the impulse required to maintain the pendulum's amplitude. This can be done by setting the energy equation equal to the impulse applied, i.e.Impulse = Change in EnergyFor example, if the total energy at the maximum displacement is E1 and the total energy at the minimum displacement is E2, then the impulse required to maintain the pendulum's amplitude is:Impulse = E1 - E2
 

1. What is impulse on a pendulum?

Impulse on a pendulum refers to the force applied to the pendulum to keep it swinging at a constant amplitude. This force is necessary to overcome the effects of friction and maintain the pendulum's motion.

2. How does the length of a pendulum affect the impulse required to maintain amplitude?

The length of a pendulum affects the period of its swing, which in turn affects the amount of impulse required to maintain amplitude. A longer pendulum has a longer period, meaning it requires less frequent but stronger impulses to maintain its motion. On the other hand, a shorter pendulum has a shorter period and requires more frequent but weaker impulses.

3. What factors can affect the amplitude of a pendulum?

The amplitude of a pendulum can be affected by various factors such as the length of the pendulum, the strength of the impulse, and the presence of external forces like air resistance. These factors can cause the amplitude to increase or decrease over time.

4. How is impulse calculated for a pendulum?

The impulse on a pendulum can be calculated by multiplying the force applied to the pendulum by the time it is applied for. This can be represented by the equation J = F x t, where J is the impulse, F is the force, and t is the time.

5. How can the amplitude of a pendulum be maintained without using external impulses?

In theory, the amplitude of a pendulum can be maintained without external impulses by making sure that the pendulum is swinging in a vacuum with no air resistance. In this scenario, the initial force applied to the pendulum will be the only force acting on it, and the pendulum will continue to swing at a constant amplitude due to the conservation of energy.

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