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what is an object that experiences simple harmonic motion?
an object that experiences a restoring force
in what direction must the restoring force of an object moving with SHM be?
towards the equilibrium position
what is the relationship between the restoring force and the distance from the equilibrium?
they are directly proportional
what is the equation linking distance from equilibrium position and restoring force?
F=-kx
what is an example of a simple harmonic oscillator?
a simple pendulum
explain the simple harmonic motion of a simple pendulum
the pendulum oscillates around a central midpoint known as the equilibrium position, and the restoring force is given by the horizontal component of gravity acting on the pendulum bob
what is the acceleration of an object experiencing simple harmonic motion proportional to?
acceleration of SHM is directly proportional to the displacement in the opposite direction
what is the equation linking displacement and acceleration of SHM?
acceleration= -angular speed² x displacement from equilibrium
what is angular speed?
the angle an object moves through per unit of time
what is the formula for angular speed?
2 pi x frequency
how can the equation for angular speed be rearranged to derive the time period of oscillations?
w=2pi x f
f= w/2 pi
T=1/f
T=1/(w/2 pi)
T=2pi/ w
what are the three formulas that can be used for simple harmonic oscillators?
x=Acos wt
v= -Awsin wt
a= -Aw²cos wt
(where A is the amplitude)
what are simple harmonic systems?
systems that oscillate with simple harmonic motion
what are examples of simple harmonic oscillators?
simple pendulum, mass-spring system
what formula is used for the period of a simple pendulum?
T= 2 pi x (root) l/g
what is the formula used to find the period of a mass-spring system?
T=2 pi x (root) m/k (where k is the spring constant)
what is the shape of a displacement-time graph of an oscillating system?
a sine or cosine curve
how can the velocity of an oscillating system be found from a displacement-time graph?
by finding the gradient of the curve as a certain point
how can a velocity-time graph be drawn?
by drawing the gradient function of the displacement-time graph
how can the acceleration of an oscillating system be found from a velocity-time graph?
by calculating the gradient at a certain point of the graph
what is resonance?
where the amplitude of a system drastically changes due to gaining an increased amount of energy from a driving force
what are examples of applications of resonance?
instruments, radios, swings
when does resonance occur?
when the driving frequency (frequency of the driving system) is equal to the natural frequency of the system
what are negative consequences of resonance?
damage to structure
what is an example of damage to structure caused by resonance?
when people crossing a bridge provide a driving frequency close to the natural frequency, the bridge will begin oscillating violently
what can be done to reduce the effects of resonance?
damping
what in damping?
where a force acts on an oscillating system and energy is lost from the system to its environment, reducing amplitude of oscillations
what are the energy transfers within a simple harmonic motion system?
kinetic energy is transferred to potential energy (which depends on the system) and back as the system oscillates
explain the transfers of energy within a simple harmonic motion system
at the amplitude, the system will have the maximum amount of potential energy, while at the equilibrium, the amount of kinetic is at its maximum
what is an undamped system?
no external forces act, so no energy is lost to the environment- total energy of the system is constant
when do free vibrations occur?
when no external force is acting on a system, so the system will oscillate at its natural frequency
what are forced vibrations?
where a system experiences an external driving force which causes it to oscillate
what are the three main types of damping?
light damping, critical damping, heavy damping
what is light damping?
also known as underdamping, this is where the amplitude gradually decreases by a small amount after each oscillation
what is critical damping?
type of damping which reduces the amplitude to zero in the shortest possible time
what is heavy damping?
also known as overdamping, where the amplitude reduces slower than critical damping but without any additional oscillations
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