# ch11 Flashcards

conditions for simple harmonic motion

force is directly proportional to displacement, and the acceleration (force) acts in the opposite direction to the displacement this tells us force is always directed to the position of equilibrium

examples of simple harmonic oscillators

springs and pendulums

what is the time for one complete swing of an oscillator

time period

what is the amplitude of an oscillation

greatest displacement from the equilibrium position

what is simple harmonic motion

an oscillation in which the restoring force on an object (acceleration of the object) is directly proportional to it’s displacement from the centre, and is directed towards the centre

equation for angular frequency, w, rate of rotation

w = 2πf rad s^-1

versions of equation for displacement applying angular velocity disp = max at t = 0 disp = 0 at t = 0

if displacement is at max when t = 0 use the equation x = Acos(2πft) -> x = Acos(wt) if displacement is 0 when t = 0 x = Asin(2πft) -> x = Asin(wt) x = displacement in metres A = amplitude t = time in seconds

how to calculate acceleration using angular velocity and the differentiation model for disp to accel

a = -w²x = -4π²f²x = d²x / dt²

what does a negative value mean when you calculate displacement of an object using the displacement equation x = Acos(2πft)

the mass is below the equilibrium at that point in instant

what is the acceleration at the point in equilibrium and why is this

acceleration at the point of equilibrium is 0, as x = 0 and a ∝ -x

a simple harmonic oscillator has an amplitude of 0.02m, the frequency of the oscillation is 1.5Hz calculate the maximum acceleration

maximum acceleration is at max displacement as a ∝ -x so x is 0.02 a = -4 * π² * f² * 0.02 = -1.8 ms^-2

displacement, x, against time graph for SH oscillator max disp at t = 0 T = 2π what type of graph is it

when amplitude A is max (max displacement) at t = 0, it’s a cosine graph

velocity, v, against time graph for SH oscillator max disp at t = 0 T = 2π what type of graph is it

the graph of velocity is the gradient of the displacement graph at t = 0, disp graph has max displacement so velocity starts at 0 the graph of velocity is a reflection of sin x in the x-axis (-sinx)

acceleration, a, against time graph for Sh oscillator max disp at t = 0 T = 2π what type of graph is it

the graph of acceleration is the gradient of the velocity graph at t = 0, displacement graph has max displacement so velocity is 0 and as velocity is 0, acceleration starts at minimum value the graph of acceleration is a reflection of cos x in the x-axis (-cosx) the graph of acceleration is also the opposite of the displacement graph

displacement, x, against time graph for SH oscillator min displacement at t = 0 T = 2π what type of graph is it

at t = 0, displacement is 0 (0 amplitude A) it’s a normal sin x graph

velocity, v, against time graph for SH oscillator min displacement at t = 0 T = 2π what type of graph is it

the graph of velocity is the gradient of the displacement graph at t = 0, disp graph has 0 displacement so velocity starts at max value it’s a cosine graph

acceleration, a, against time graph for SH oscillator min displacement at t = 0 T = 2π what type of graph is it

the graph of acceleration is the gradient of the velocity graph at t = 0, displacement graph has 0 displacement so velocity is at max acceleration graph is the opposite of the displacement graph, but as displacement is 0, acceleration starts at 0 a = -x acceleration is a reflection of the displacement graph

value of velocity when displacement is maximum

0

value of velocity when displacement is 0

maximum

value of displacement when velocity is 0

maximum

value of displacement when velocity is maximum

0

what equation can be used to calculate acceleration, and thus velocity and displacement, from iterative models and calculations

F = ma

maximum value of acceleration graph

w²A

maximum value of velocity graph

wA