Question

physics
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unit 10: energy in simple harmonic motion

1. \define the definitions of an underdamped system and critically damped system below.

underdamped: there is moderate friction on the pendulum such that it returns to rest at equilibrium after one full oscillation.
critically damped: the friction in the pendulum is substantial such that after the initial displacement, the pendulum swings at the minimal speed to equilibrium but doesnt pass through it.

1. \the graph below shows the motion of a pendulum over time. draw two new lines on this graph:

• one line to represent an underdamped pendulum.
• one line to represent a critically damped pendulum.

label each line appropriately.

1. describe a real world system that benefits from damping.

Explanation:

Question 3

• Underdamped System: A system where damping is small enough that it oscillates around the equilibrium position after a disturbance, with the amplitude of oscillations gradually decreasing over time (due to non - zero but low damping force, e.g., a pendulum in air with minimal friction).
• Critically Damped System: A system where the damping is such that it returns to the equilibrium position in the shortest possible time without oscillating. The damping force is just enough to prevent oscillations, like a door closer with the right damping to make the door close without bouncing.

• Underdamped Line: It should be a sinusoidal - like curve (since it oscillates) with decreasing amplitude over time. Start from the initial point (the 'x' mark), and draw a wave - like curve where the height of each peak (and depth of each trough) gets smaller as time (t - axis) increases.
• Critically Damped Line: It should be a curve that starts at the initial point (the 'x' mark) and approaches the equilibrium line (the horizontal line) monotonically (without any oscillations), getting to the equilibrium as quickly as possible.

A car's suspension system benefits from damping. The suspension has springs and shock absorbers (which provide damping). When the car goes over a bump, the springs compress and then would oscillate without damping. The damping from the shock absorbers reduces these oscillations, providing a smoother ride, preventing the car from bouncing up and down continuously, and also improving the car's stability and control. Another example is a building's structure during an earthquake. Damping systems in buildings (like tuned mass dampers or viscous dampers) reduce the amplitude of the building's oscillations, protecting the structure from damage.

Answer:

• Underdamped: A system with low damping that oscillates (with decreasing amplitude) about equilibrium after a disturbance.
• Critically Damped: A system with damping that returns to equilibrium quickly without oscillating.

Question 4