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Simple Harmonic Motion. Chapter 10 Sections 10.1 – 10.6. Simple harmonic motion. Simple harmonic motion is a cyclic motion produced by a a) mass & spring b) pendulum. Simple harmonic motion animation. Amplitude. Amplitude. Displacement x. 0. time t. Vocabulary.
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Simple Harmonic Motion Chapter 10 Sections 10.1 – 10.6
Simple harmonic motion Simple harmonic motion is a cyclic motion produced by a a) mass & spring b) pendulum. Simple harmonic motion animation
Amplitude Amplitude Displacement x 0 time t Vocabulary Period T = time for one cycle Frequency f = number of cycles in one second Displacement x = distance from equilibrium position Amplitude A = maximum displacement
frequency in Hertz, Hz period in seconds, s angular frequency in radians/second, s-1 displacement in meters, m Simple harmonic motion relationships
Mass and spring system Spring force equation is Fspring = - k x The minus sign shows that the spring is pulling the block back to the equilibrium position. The spring constant k is the stiffness of the spring. Unit for k is N/m angular frequency Period depends on the mass and the stiffness of the spring.
Simple harmonic motion Object reverses direction when displacement x is maximum Force is maximum Acceleration is maximum Velocity is zero
Pendulum Pendulum length is L angular frequency period of oscillation T The period depends length of the string and gravity.
Energy and simple harmonic motion Stretching and compression of a spring or the raising of a pendulum increases the potential energy of the system. Both spring and gravity forces are conservative forces that provide lossless energy transfers between potential energy and kinetic energy. Potential energy is maximum when the displacement is maximum. Kinetic energy is maximum when the velocity is maximum.
Resonance Vibrating systems vibrate at their natural frequency. Energy can be continually added to the system by a small external force with a frequency that matches the system's natural frequency. The added energy causes the vibration amplitude to continually increase. The result is that a small force can produce a large amplitude motion. This effect is called resonance. A small driving force produces large amplitude oscillations of a playground swing.
