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Q no. |
Answer |
Commentary |
|
1 |
E |
Match like terms with x = A cos (2pft) don’t worry about the “sin” it’s just a phase relationship x = a sin (wt) don’t panic about the “a” representing “A” then amplitude, A = a and angular speed, w = 2pf (i) at max amplitude acceleration is max … = w2A (ii) momentum = mv = m (w Ö A2 – x2) max v is when x=0 so mv = mwA (iii) KE = ½ mv2 = ½ m (wA)2 (see above) (iv) w = 2pf rearranges to give f = w / 2p |
|
2 |
B |
(i) object has greatest speed when x = 0. t2 is closer to x = 0 so FALSE (ii) greatest acceleration when x = A, t1 is closer to A (iii) at t1 object is accelerating into the centre (it’s ALWAYS doing that except when x=0) (iv) no – it has the least acceleration when x = 0 so the acceleration is decreasing (even though it is still accelerating) |
|
3 |
D |
a = -w2x if f = b/2p and w = 2pf then rearrange both to give w = b at extremity – x = A therefore acceleration = -b2A |
|
4 |
C |
Spring system – T is unaltered (no g in the formula) so can only be B or C Pendulum – T depends upon g so must be C [also: (Ö 10 /Ö 40) = ½ ] |
|
5 |
A |
divide the two expression for time period for a simple
pendulum: most terms cancel to give: Ö l / Ö (I + 1.8) = T / 2T rearrange to give l = 0.6m |
|
6 |
C |
Beat frequency is the frequency of the consecutive instants when the pendulums are in phase. fbeat = f1
– f2 or 1/Tbeat = 1/T1 – 1/T2 rearranges to give Tbeat = 198 seconds The longer pendulum has a T = 2s In 198 seconds the longer pendulum will oscillate 99 times |
|
7 |
B |
At x = 0 only energy is KE = ½ mv2 This is equal to total energy via conservation At x=0 v reduces to v = 2pfA KE = ½ m(2pfA)2 |
|
8 |
D |
Changing amplitude of driving force will change amplitude, energy and power but not frequency |
|
9 |
C |
Conductor moving in a magnetic field will lead to eddy currents which will oppose the motion (Lenz’s law – remember magnets falling down the copper piping) |
|
10 |
|
x = 0.05 sin 6t match like terms with x = A cos (2pft) don’t worry about sin or cos – it just a phase difference so: A = 0.05m w = 6 f = 6/2 p T = 1/f T = 2p / 6
max a is when x = A
a = w2A = 62
X 0.05 = 1.8ms-1 Hookes law says that F is proportional to extension (ie displacement of mass) So: F = kx where k is the constant of proportionality F = ma rearranges to give a = -(k/m)x negative because when you stretch a spring the force opposes the displacement – which is a definition of SHM Match like terms then w2 = (k/m) w = Ö(k/m) = 2pf rearranges to give f = (1/2p)Ö(k/m) time period T = 1/f = 2pÖ(m/k) forced vibrations: when an external periodic force is applied to a system that is free to oscillate resonance: when the forced frequency of vibration = natural frequency of the system – leads to a sharp peak in the amplitude of vibrations damping: any periodic loss of energy from a vibrating system at greater damping the resonance peak is broadened over a greater range of frequencies and the amplitude of the resonance peak is reduced ( see Breithaupt) |