what is the equation for the restoring force, F
f = -kx
what is the restoring force
- for a system moving with simple harmonic motion
- it is the force that tries to return the object to its equilibrium position
what is k in that equation
- the spring constant
- its value is dependent on the oscillating system
why is there a negative sign in the equation
- to indicate that acceleration will always be to the centre of oscillation
- as the object moves away from the equilibrium point, it will begin decelerating
- as the force is acting in the opposite direction
what is the definition of simple harmonic motion
- when a system is oscillating such that a force is trying to return the object to its centre position
- and this force is proportional to the distance from that centre position
- in simple terms, the restoring force, F = -kx
what is the equation for calculating the period of the oscillations of a mass m, subject to hookes law restoring force
T = 2 pi * the root of (m/k)
what is the equation for the period of a pendulum
T = 2 pi * the root of (l/g)
what is l and g in that equation
- l = the length of the pendulum string
- g = gravity
what is the definition of oscillation
to undertake continuously repeated movements
what is the definition of a period
the time it takes for one complete oscillation
what does it mean if an oscillation is isochronous
the period is independent of the amplitude
if a 500g toy train is attached to a string with spring constant of 100Nm-1 and made to oscillate horizontally, what force acts on the train when it has an amplitude position 8cm from equilibrium
- F = -kx
- k = 100
- x = 8cm = 0.08m
- -100 * 0.08 = -8N
how fast will the train accelerate whilst at this amplitude position
- F = ma
- a = F/m
- -8/0.5 = -16ms-2
What actually is simple harmonic motion
- when acceleration
- which is always acting towards the equilibrium
- is directly proportional to the displacement from the equilibrium
