A mass of 0.40 kg, which is resting on a frictionless horizontal surface and attached to a spring with a spring constant of 40.0 N/m, is set into simple harmonic motion by stretching the spring to 0.25 m and releasing it. What is Hooke’s Law? What is the magnitude of the force required to stretch the spring 0.25m? Which direction does the force point?
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.
A mass of 0.40 kg, which is resting on a frictionless horizontal surface and attached to a spring with a spring constant of 40.0 N/m, is set into
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What is Hooke’s Law?
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What is the magnitude of the force required to stretch the spring 0.25m?
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Which direction does the force point?
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Which one of Newton’s Laws would help you find the acceleration of the mass?
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What is the magnitude of the acceleration of the mass when at its maximum displacement from the equilibrium position? Would the mass experience maximum or minimum acceleration at this position?
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What is the magnitude of the amplitude of the system? Would the magnitude of the amplitude change if the system was compressed instead of stretched?
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What is the position of the mass when the system experiences its greatest force?
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What is the magnitude of the force when the position of the mass is half the maximum amplitude?
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What is the speed of the mass when its position is equal to its amplitude?
10.In general terms, what is the speed of the mass when it returns to its equilibrium position? (for example, 2*vmax, 0, vmin)
11.Write an equation for the total energy of the system at any position.
12.Write an equation for the energy of the system at its maximum displacement.
13.Write an equation for the energy of the system at its maximum velocity.
14.How is the energy found in questions 11, 12, and 13 related to each other? Which law makes this true?
15.Calculate the total energy in the system.
16.Calculate the total energy in the system when the displacement is half the amplitude.
17.Calculate the magnitude of the maximum velocity.
18.Calculate the magnitude of the velocity when the displacement is half the amplitude.
19. Which is not an example of approximate simple harmonic motion? Why?
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A ball bouncing on the floor.
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A child swinging on a swing.
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A piano string that has been struck.
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A car's radio antenna as it waves back and forth.
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