Harmonic Motion Theory: What is for a harmonic oscillator (in terms of the perio

Question

Harmonic Motion Theory: What is for a harmonic oscillator (in terms of the period)? What is for a spring? If you increase the amplitude, what happens to the period? o If you increase the mass, what happens to the period? o If you increase the spring constant, what happens to the period? What is for a simple pendulum? If you increase the amplitude, what happens to the period? o If you increase the mass, what happens to the period? o If you increase the length, what happens to the period? For a harmonic oscillator o What is the formula for position over time? Sketch a graph. o What is the formula for velocity over time? Sketch a graph. o What is the velocity when the position is a maximum? o What is the position when the velocity is a maximum?

Explanation / Answer

1) = 2pi/T   where T = Period

2) = sqrt(k/m) where k = spring constant

     T = 2pi*sqrt(m/k)

a) No effect of amplitude

b) With increase the mass, Period will increase

c) With increase the spring constant, Period will decrease

3) = sqrt(g/L) where L = length

     T = 2pi*sqrt(L/g)

a) No effect of amplitude

b) No effect of mass

c) With increase the length, Period will increase

4) a) x = A*cos(t)

b) v = dx/dt = -A*sin(t)

c) when position is maximum ====> t = 0 ====> Then Velocity = 0

d) when velocity is maximum ====> t = 90 degree ====> Then position = 0

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