Question

C3. (a) A pendulum is to be used for a clock (0) What length of string is required for this pendulum if it is to complete one full oscillation in 2S? (i) If the length of the pendulum was increased by 5 cm, would the clock run fast or slow? Explain your thinking [41 (b) () Explain why the amplitude of a real pendulum decreases with time. (i) To stop the amplitude decreasing the pendulum could be given a tap at regular intervals. What frequency would be most appropriate for this tapping? Hence define the phenomenon of resonance and give an example where resonance can be destructive (c) If a spring-mass system was used as a clock, what spring constant would be required to give a period of 2 s, when a mass of 400 g was hung on the spring? (d) If the pendulum and spring-mass system above (each with period 2 s) were taken to a planet where gravity is 0.8 of the value on earth:- (i) state and explain whether the pendulum would keep the correct time. (ii) state and explain whether the spring-mass would keep the correct time. (ii) For the above system(s) that do not keep the correct time, calculate the new period and how far out they would be in 24 hours.
D/iii

Answer 1

D)

The spring mass will keep correct time.

because k/m = w^2... independent of g

but T = 1/2pi (L/g)^0.5 .. dependent on g and hence will change time

New T

T2 / T1 = (g1/g2)^0.5 = (1/0.8)^0.5 = 1.118 sec

error of 0.118 sec for every second

error of 0.118 x 24 x 3600 = 10195 sec in 24 hrs

error of 2.83 hours in 24 hours