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Simple Harmonic Motion

Simple Harmonic Motion. Simple harmonic motion: Motion that follows a repetitive pattern, caused by a restoring force that is proportional to displacement from the equilibrium position. In the case of this simple pendulum, what is the restoring force?. Simple Harmonic Oscillator: . F = - kx.

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Simple Harmonic Motion

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  1. Simple Harmonic Motion Simple harmonic motion: Motion that follows a repetitive pattern, caused by a restoring force that is proportional to displacement from the equilibrium position. In the case of this simple pendulum, what is the restoring force?

  2. Simple Harmonic Oscillator: F = - kx Period of oscillation (T) depends upon the mass and force constant: m k T = 2π

  3. A small bug (0.30 g) is caught in a spider web and causes the web to vibrate with a frequency of 15 Hz. A) What would be the spring constant of this web? B) If the web trapped a bug that is 1/3 as massive, what frequency would you predict the web to vibrate with? Solve quantitatively to assess your prediction. m k A) T = 2π m = .30 g f = 15 Hz k = 4π2m T2 = 2.7 N/m T = 1/f = .067 s B) 26 Hz

  4. Simple Pendulum: a pendulum in which the mass is considered to be concentrated in the bob. In addition, the angle of displacement is relatively small (less than 15˚) The period of the pendulum will be dependent only upon gravity and the length of the pendulum: L g T = 2π

  5. What must be the length of the simple pendulum in a grandfather clock that advanced 1.0 s with each cycle of the pendulum? L = T2g 4π2 L g T = 1.0 s T = 2π = .25 m How long would it take that same clock to complete one cycle if it were used on the moon (g = 1.7 m/s2)? = 2.4 s L g .25 m 1.7 m/s2 T = 2π = 2π

  6. A 10.0 kg mass stretches a spring 5.00 cm. What would be the period of oscillation of that spring is 18.0 kg were attached to it and released? A .50 kg mass at the end of a spring vibrates 3.0 times per second with an amplitude of .15 m. A) What is the spring constant of the spring? B) What is the speed of the block when the spring is compressed .15 m? A mass causes a spring to oscillate with a frequency of .88 Hz. When .600 kg is added to the spring, its frequency is .60 Hz. What was the original mass?

  7. You want to make pendulum clock so that a single swing one time across will advance the clock one second. How long should you make the pendulum? What is the period of a simple pendulum that is .250 m long. What would be the period be in an orbiting space shuttle? What is the frequency of a simple pendulum with a 2.00 kg bob and a length of .650 m? A simple pendulum on earth has a period of 1.00 s on earth. What is the period of that pendulum on the moon where g = 1.67 m/s2?

  8. A pendulum on earth has a period of .00670 s on the surface of the earth. Aboard a launching rocket ship, its period changes to .00310 s. What is the acceleration of the launching rocket ship? A pendulum of length 2.50 m is used near the “surface” of Saturn and completes 4.00 full cycles in 11.8 s. What must be the acceleration due to gravity on Saturn? A pendulum used on earth is timed for 6.0 s. If the length of the pendulum was measured as .994 m, how many cycles did it complete?

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