ws17 - in a swing if you want them to go higher you only...

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Worksheet 17: Oscillations Questions 1. Simple harmonic motion is when an object oscillates with a frequency which is in- dependent of amplitude. It is characterised by the fact that the acceleration of the object is proportional to its velocity: a + ω 2 x = 0 2. In one period, an object travels 4 A distance. 3. Some examples of SHO include: a simple pendulum, object Foating in water, mass on a spring, etc. 4. ω f = ω 0 , E f = 4 E i , v max,f = 2 v max,i , a max,f = 2 a max,i 5. The resonant frequency is just the natural frequency of oscillation for a SHO. If you drive an object to oscillate at a frequency other than its natural frequency (e.g. ω = r k m for mass-spring system), then the amplitude of oscillation is much smaller than if you drive it to oscillate at the natural frequency. Think about pushing someone
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Unformatted text preview: in a swing, if you want them to go higher, you only push at the right times. Problems 1. A mass is connected to two springs. (a) T = 2 π r M k 1 + k 2 (b) x ( t ) = (1 m ) cos( ω t ) (c) E tot = 1 2 ( k 1 + k 2 ) x 2 max = 12 . 5 J (d) v max = 5 m/s 2. A heavy is suspended by a peg; the period of oscillation is T = 2 π r 7 L 12 g 3. A small mass sits at the bottom of a frictionless hemispherical bowl of radius R . The period of oscillaition is T = 2 π r R g 4. A thin rod is free to rotate about a pivot and is connected to a spring on one end. The period of oscillation is T 2 = (2 π ) 2 ( L 2 + 3 r 2-3 rL ) M 3 kr 2 1...
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