simple harmonic motion (shm)
DESCRIPTION
Simple Harmonic Motion (SHM). (and waves). What do you think Simple Harmonic Motion (SHM) is???. Defining SHM. Equilibrium position Restoring force Proportional to displacement Period of Motion Motion is back & forth over same path. Θ. F g. Describing SHM. Amplitude. Θ. F g. - PowerPoint PPT PresentationTRANSCRIPT
Simple Harmonic Motion (SHM)
(and waves)
• What do you think Simple Harmonic Motion (SHM) is???
Defining SHM
• Equilibrium position
• Restoring force– Proportional to
displacement
• Period of Motion• Motion is back &
forth over same path
Describing SHM
• Amplitude
Fg
Θ
Describing SHM
• Period (T)
• Full swing– Return to
original position
Fg
Θ
Frequency
• Frequency- Number of times a SHM cycles in one second (Hertz = cycles/sec)
• f = 1/T
SHM Descriptors
• Amplitude (A)– Distance from
start (0)
• Period (T)– Time for
complete swing or oscillation
• Frequency (f)– # of oscillations
per second
Oscillations
• SHM is exhibited by simple harmonic oscillators (SHO)
• Examples?
Examples of SHOs
• Mass hanging from spring, mass driven by spring, pendulum
SHM for a Pendulum
• T = period of motion (seconds)
• L = length of pendulum
• g = 9.8 m/s2
2L
Tg
Energy in SHO
• EPE = ½ k x2
• KE = ½ m v2
• E = ½ m v2 + ½ k x2
• E = ½ m (0)2 + ½ k A2
E = ½ k A2
• E = ½ m vo2 + ½ k (0)2
E = ½ m vo2
Velocity
• E = ½ m v2 + ½ k x2
• ½ m v2 + ½ k x2 = ½ k A2
• v2 = (k / m)(A2 - x2) = (k / m) A2 (1 - x2 / A2)
– ½ m vo2 = ½ k A2
– vo2 = (k / m) A2
• v2 = vo2 (1 - x2 / A2)
• v = vo 1 - x2 / A2√
Damped Harmonic Motion
• due to air resistance and internal friction
• energy is not lost but converted into thermal energy
• A: overdamped
• B: critically damped
• C: underdamped
Damping
• occurs when the frequency of an applied force approaches the natural frequency of an object and the damping is small (A)
• results in a dramatic increase in amplitude
Resonance