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SHM multi choice questions from old exam collection


Q no.





Match like terms with x = A cos (2pft) dont worry about the sin its just a phase relationship

x = a sin (wt) dont 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 A2 x2) max v is when x=0 so mv = mwA

(iii) KE = mv2 = m (wA)2 (see above)

(iv) w = 2pf rearranges to give f = w / 2p



(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 (its 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)



a = -w2x if f = b/2p and w = 2pf then rearrange both to give w = b

at extremity x = A therefore acceleration = -b2A



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: ( 10 / 40) = ]



divide the two expression for time period for a simple pendulum: most terms cancel to give:

l / (I + 1.8) = T / 2T rearrange to give l = 0.6m



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



At x = 0 only energy is KE = mv2

This is equal to total energy via conservation

At x=0 v reduces to v = 2pfA

KE = m(2pfA)2



Changing amplitude of driving force will change amplitude, energy and power but not frequency



Conductor moving in a magnetic field will lead to eddy currents which will oppose the motion (Lenzs law remember magnets falling down the copper piping)



x = 0.05 sin 6t match like terms with x = A cos (2pft) dont 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 = (k/m) = 2pf rearranges to give f = (1/2p)(k/m)


time period T = 1/f = 2p(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)