Chapter 18 - Simple harmonic motion Flashcards
What is the equation for the phase difference of two objects undergoing simple harmonic motion?
T
where Δt is the constant time gap between two oscillating objects
What is simple harmonic motion?
Oscillating motion in which:
• acceleration is always in the opposite direction to the displacement
• a ∝ -x 2
with constant of proportionality ω
(An oscillating object speeds up as it returns to its equilibrium position and slows down as it moves away from the equilibrium).
What is the relationship between the period and frequency of an oscillation and the amplitude in SHM?
There is none.
In SHM, the frequency and period of an oscillation are independent of the amplitude (i.e. constant for a given oscillation).
In SHM, we use the magnitude of angular velocity, ω, which is defined as…
…angular frequency.
What is the restoring force?
A force which acts to bring a body to its equilibrium position.
This force is present in SHM.
The restoring force depends on the system.
What factors affect the period of an oscillation of a mass-spring system?
Hint: It is shown by the equation
- Mass (m↑, T↑)
- Stiffness (Spring constant) (k↑, T↓ )
What factors affect the period of an oscillation of a simple pendulum?
Hint: It is shown by the equation
- Length of rod/string (L↑,T↑)
- g (g↑, T↓)
What is the equation for the kinetic energy of a simple harmonic oscillator?
1 2 2
Ek = —k(A - x )
2
What is the equation for the velocity and speed of an object undergoing SHM?
What is the equation for the maximum speed of an object undergoing SHM?
v = ±ωx v = velocity
v = ωx v= speed
vmax = ωA
What is the equation for the acceleration of an object undergoing SHM?
What is the equation for the maximum acceleration of an object undergoing SHM?
2
a = 𝜔 x
2
amax = 𝜔 A
What is free oscillation?
Oscillation of an object caused by a restoring force with no external forces (therefore, constant amplitude, constant total energy).
An object oscillating at its natural frequency.
What is natural frequency?
The frequency that a system oscillates without the presence of external forces.
(The frequency of free oscillations of an oscillating system).
What is a periodic force?
A force that varies regularly in magnitude with a definite time period.
A force applied at regular intervals.
What is a forced oscillation?
The oscillation of an object subjected to an external periodic force.
What is driving/applied frequency?
The frequency of a periodic force.
An object undergoing forced oscillation oscillates at the _______ frequency of the _______ force rather than its ______ frequency.
An object undergoing forced oscillation oscillates at the driving/applied frequency of the periodic force rather than its natural frequency.
What is damping?
Any effect that tends to reduce the amplitude of oscillations (e.g. friction).
What is a damped oscillation?
One where the amplitude of the oscillations decrease over time as a result of resistive forces.
What is light damping?
Damping in which the resistive forces acting on an oscillating mass are small. The amplitude decreases over a period of time during oscillation.
What is critical damping?
When the displacement of an object decreases to zero in the shortest time possible without any oscillation.
What is heavy damping?
When the system returns to the equilibrium position very slowly without any oscillation.
What is resonance?
The condition in which an object or system is subjected to an oscillating force having a frequency (driving frequency) equal to its natural frequency. This causes increasing amplitude of oscillation up to the resonant frequency.
What is resonant frequency?
The frequency of oscillation at which the energy supplied by an external driving force is equal to the energy lost per cycle (to resistive forces). The amplitude stops increasing. The amplitude has reached a maximum.
How do the Barton’s Pendulums show resonance?
The small pendulum with the same length string as the heavy ‘driver’ pendulum oscillates at the same frequency as the driving frequency (frequency of driver pendulum)
