Further Mechanics and Thermal Physics (2): SHM Flashcards
What is the definition of the equilibrium position for oscillating bodies?
The point at which the body will eventually come to a standstill
Describe the how the displacement of an oscillating object changes over one full cycle after being released form equilibrium?
- Displacement decreases as it returns to equilibrium
- Displacement reverses and increases as it moves away from the equilibrium in the opposite direction
- Displacement decreases again as it returns to equilibrium
- Displacement increases as it moves away from equilibrium towards its starting position
What is the definition of amplitude?
The maximum displacement of an oscillating object from its equilibrium position
If the amplitude is constant and there are no frictional forces, how are the oscillations described?
As free vibrations
What is the definition of Time Period, T?
The time taken for one complete cycle of oscillation (when the object passes through the same position in the same direction again)
What is the definition of the frequency of an oscillating object?
The number of full cycles per second made by an oscillating object
What is the equation for the phase difference between two oscillating objects in radians?
phase difference in radians = 2(pi)(delta)t/T
where:
(delta)t is the time between successive instants when the two objects are at maximum displacement in the same direction
As an object moves away from equilibrium, how does its speed change?
Speed decreases
As an object moves towards equilibrium how does its speed change?
Speed increases
How does the displacement of an object that follows SHM change when it is released from a maximum displacement x?
The object oscillates between +x and -x following the motion of a cos wave or a sine wave (depends on the situation given)
Where does the force always act towards in SHM?
The equilibrium position
Where does acceleration always act towards in SHM?
The equilibrium position
How does the velocity of an object that follows SHM change when it is released from a +ve displacement x?
The velocity follows the motion of a -ve sine wave (the gradient at each point of a displacement-time graph)
- Initially, the object travels away from the +ve displacement point, therefore initial velocity is -VE
- The object reaches a peak, maximum negative velocity point, as it goes past the equilibrium position
- The objects velocity becomes less negative as it reaches the -ve maximum displacement on the other side (this is when the graph goes through 0)
- The velocity then becomes increasingly positive as the object oscillates back down to the equilibrium position and reaches a second peak which is the same magnitude as the first but +ve
- The velocity then decreases down to zero as it returns to its initial displacement position
How does the acceleration if an object that follows SHM change when it is released from a +ve displacement x?
The acceleration follows the motion of a -ve cos wave (or the gradient at each point of a velocity-time graph OR opposite to the graph of displacement-time)
- Initially, acceleration is -ve as you have a positive displacement
- The acceleration decreases to 0 when as the object passes through its equilibrium position as the velocity is at a maximum
- The acceleration increases in the positive direction (acts in the positive direction) as the object gains -ve displacement
- Acceleration reaches a maximum at the maximum -ve displacement then decreases back down to 0 as the object passes through the equilibrium position again
- Finally, the acceleration increases in the -ve direction a the object returns to its original displacement
The gradient of what graph sows the variation of velocity with time?
displacement-time
The gradient of what graph shows the variation of acceleration with time?
velocity-time
In SHM in what way does the acceleration always act relative to the displacement?
The acceleration always acts in the opposite direction to the displacement
What is the definition of SHM?
The oscillating motion in which the acceleration is proportional to the displacement and always in the opposite direction to the displacement
What is the relationship between acceleration and the displacement in SHM?
a is directly proportional to -x
OR
a = -constant multiplied by displacement x
What does the constant of proportionality between acceleration and displacement in SHM depend on?
Depends on the time period of the oscillations
What does omega stand for in SHM?
The angular frequency
What is the equation for angular frequency of an object in SHM?
omega = 2(pi)/T
What is the equation for simple harmonic motion?
a = -(omega)^2x
where
x - displacement
omega - angular frequency
Does the time period of an object in SHM effect its amplitude and vice versa?
NO - the two values are independent of one another
What is maximum displacement equivalent to in SHM?
The amplitude of the oscillations
x(max) = …?
+/- ampltiude
When the maximum displacement = +A, what is the equation for SHM?
a = -(omega)^2A
When the maximum displacement = -A, what is the equation for SHM?
a = (omega)^2A
Does circular motion follow the same motion as SHM?
yes
How do you prove that the constant of proportionality for the acceleration of an SHM system is (omega)^2?
Using a set up where you compare the circular motion of a ball with SHM of a pendulum -> have a projector which shows that the shadows of both of the items remain in phase
- Start the two, ball and bob, in the same position with P having the coordinates (rcos(theta), rsin(theta))
- They will follow the same motion
Of ball on turntable
a = -v^2/r
as minus sign indicates direction is towards the centre of the circle
a = -(omega)^2r
component of acceleration parallel to the screen ->
ax = acos(theta)
ax = -(omega)^2rcos(theta)
as x = rcos(theta)
ax = -(omega)^2x