Examination Style Questions 5 from Oscillations note

One particle oscillating in simple harmonic motion has ten times the total energy of another particle, but the frequencies and masses are the same. Calculate the ratio of the amplitudes of the two motions.

Solution:

Reference: Examination Style Questions 5 from Oscillations note

9702/May Jun/11/2011/Q5

The diagram shows an experiment to measure the speed of a small ball falling at constant speed
through a clear liquid in a glass tube.

There are two marks on the tube. The top mark is positioned at 115 ± 1 mm on the adjacent rule
and the lower mark at 385 ± 1 mm. The ball passes the top mark at 1.50 ± 0.02 s and passes the
lower mark at 3.50 ± 0.02 s.

The constant speed of the ball is calculated by (385 – 115) / (3.50 – 1.50) = 270 / 2.00 = 135 mms^-1.

Which expression calculates fractional uncertainty in the value of this speed?

Solution:
Answer: A

Speed v = Distance s / Time t

Δv / v = (Δs / s) + (Δt / t)

Fractional uncertainty of speed = Δv / v

Distance s = 385 – 115 = 270 mm

Δs = ± (1 + 1) = ± 2 mm

Time t = 3.50 – 1.50 = 2.00s

Δt = ± (0.02 + 0.02) = ± 0.04 s

Reference: PYQ - May/Jun 2011 Paper 11 Q5