A 0.74-kg cart is attached to the end of a spring with spring constant 5 N/m at the end of a frictionless, horizontal track. The cart is displaced a distance of -0.11 m from its equilibrium position and released. Draw a sketch of the situation, labeling all of the physical quantities given in the problem. Sketch position-time, velocity-time, and acceleration-time graphs which represent the motion of this object. Draw a qualitative a work-energy bar chart which represents the energy present in a system consisting of the cart, the spring, and the track. Choose the moment before the cart is released as your initial state and the moment the cart first passes through its equilibrium position as your final state. Solve for (a) the period of the cart's vibrational motion and (b) the maximum kinetic energy of the cart. Show all work needed to solve for these two quantities. Explain how you arrived at your solution (not just what you did, but why you did everything). Evaluate your solution. Describe how you evaluated your answer and whether or not you think your answer is reasonable.
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
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A 0.74-kg cart is attached to the end of a spring with spring constant 5 N/m at the end of a frictionless, horizontal track. The cart is displaced a distance of -0.11 m from its equilibrium position and released.
- Draw a sketch of the situation, labeling all of the physical quantities given in the problem.
- Sketch position-time, velocity-time, and acceleration-time graphs which represent the motion of this object. Draw a qualitative a work-energy bar chart which represents the energy present in a system consisting of the cart, the spring, and the track. Choose the moment before the cart is released as your initial state and the moment the cart first passes through its equilibrium position as your final state.
- Solve for (a) the period of the cart's vibrational motion and (b) the maximum kinetic energy of the cart. Show all work needed to solve for these two quantities. Explain how you arrived at your solution (not just what you did, but why you did everything).
- Evaluate your solution. Describe how you evaluated your answer and whether or not you think your answer is reasonable.
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