Week 5 free and forced vibrations

oscillatory motion

the repetitive back-and-forth movement of an object around a central equilibrium point (ex. pendulum); are all perodic motion

periodic motion

any movement that repeats itself over equal time intervals (ex. clocks); are not all oscillatory motion

finding the period of the pendulum

T=2pi x sqrt(L/g)

T=period, L=length of string,g=gravitational acceration (9.81 m/s)

does mass of the pendulum affect the period?

no

if you displace the pendulum one small and one larger, which would have bigger displacement?

the displacement doesn’t affect the period (displacement isn’t a variable to find the period)

angular frequency

the angular displacement (change in angle) of any element of the wave per unit time (rad/period)f

equation to find phase difference in radians

2pi(change in t)/T

free oscilation

no restrictions, constant amplitude

damped oscillations

any oscillating system where friction or air resistance is present, the amplitude decreases

types of damped oscillations

critical damping, light damping, and deavy damping

forced vibrations

aka forced oscillations, when a periodic force is applied to it (ex. pushing someone on a swing)

natural frequency

the system oscillates without a periodic force being applied to it