Oscillations and Waves

Transcription

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2 Oscillations and Waves Periodic Motion Simple Harmonic Motion Connections between Uniform Circular Motion and Simple Harmonic Motion The Period of a Mass on a Spring Energy Conservation in Oscillatory Motion The Pendulum

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4 Simple Harmonic Motion Simple harmonic motion occurs when the net force along the direction of motion obeys Hooke s law when the net force is proportional to the displacement from the equilibrium point and is always directed toward the equilibrium point.

5 Not all periodic motions over the same path can be classified as simple harmonic motion.

6 The motion of an object suspended from a vertical spring is also simple harmonic. In this case the force of gravity acting on the attached object stretches the spring until equilibrium is reached and the object is suspended at rest.

7 The following three concepts are important in discussing any kind of periodic motion: The amplitude A is the maximum distance of the object from its equilibrium position. The period T is the time it takes the object to move through one complete cycle of motion. The frequency f is the number of complete cycles or vibrations per unit of time, and is the reciprocal of the period ( f = 1/T ).

8 The acceleration of an object moving with simple harmonic motion: Constant- Acceleration Equations Don t Apply

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10 When an object moving in simple harmonic motion is at its maximum displacement from equilibrium, which of the following is at a maximum? (a) velocity (b) acceleration (c) kinetic energy. Pre-Class

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12 ELASTIC POTENTIAL ENERGY

13 Potential and Kinetic Energy

14 Conservation of Mechanical Energy with conservative forces with non-conservative forces Rotational KE must also be included in situations where there is torque.

15 Velocity as a Function of Position Solve for v:

16 Finding maximum velocity, minimum velocity, and maximum force. a) Max Velocity: When x = 0 b) Min Velociy: x = A c) When x = A because acceleration is greatest.

17 Problem A N car starts at rest and rolls down a hill from a height of 10.0 m. It then moves across a level surface and collides with a light spring-loaded guardrail. (a) Neglecting any losses due to friction, and ignoring the rotational kinetic energy of the wheels, find the maximum distance the spring is compressed. Assume a spring constant of 1.0 x 10 6 N/m. (b) Calculate the maximum acceleration of the car after contact with the spring, assuming no frictional losses. (c) If the spring is compressed by only 0.30 m, find the change in the mechanical energy due to friction.

18 Relating SHM to Circular Motion

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20 Period and Frequency of Circular Shadow

21 Period of a Mass/Spring System Notice frequency not dependent on Force. Measured in Hertz...Hz

22 A 1.30 x 10 3 kg car is constructed on a frame supported by four springs. Each spring has a spring constant of 2.00 x 10 4 N/m. If two people riding in the car have a combined mass of 1.60 x 10 2 kg, find the frequency of vibration of the car when it is driven over a pothole in the road. Find also the period and the angular frequency. Assume the weight is evenly distributed.

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24 Pre-Class

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26 Quote of the Day A cement mixer collided with a prison van on I-95. Motorists are asked to be on the lookout for sixteen hardened criminals.

27 Daily Objective SWBAT utilize the quantities of mass, amplitude, and length IOT determine the period, linear frequency, and angular frequency of a Simple Pendulum in Simple Harmonic Motion.

28 The Simple Pendulum

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30 What does the period depend upon?

31 A desktop toy pendulum swings back and forth once every 1.0 s. How long is this pendulum? (Answer 0.25 m)

32 What is the free-fall acceleration at a location where a 6.00 m long pendulum swings through exactly 100 cycles in 492 s? (Answer 9.79 m/s 2 )

33 P R O B L E M You need to know the height of a tower, but darkness obscures the ceiling. You note that a pendulum extending from the ceiling almost touches the floor and that its period is 12 s. How tall is the tower?

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