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A mass on a string of unknown length oscillates as a pendulum with a period of 4.9 s . Parts A to
D are independent questions, each referring to the initial situation.
Part B
What is the period if the string length is doubled?
Part C
What is the period if the string length is halved?
Part D
What is the period if the amplitude is doubled?
Solution
Time period of a pendulum T = 2*pi*sqrt(L/g)
part(B)
(T2/T1)^2= L2/L1
if L2 = 2*L1
(T2/T1)^2 = 2
T2 = T1*sqrt2
T2 = 4.9*sqrt2
time period T2 = 6.9 s
======================
part C
if L2 = L1/2
(T2/T1)^2 = 1/2
T2 = T1/sqrt2
T2 = 4.9/sqrt2 = 4.9/1.41
T2 = 3.5 s
==============================
part D
time period is independent of amplitude
time period remains same 4.9 s

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A mass on a string of unknown length oscillates as a pendulum with a p.docx

  • 1. A mass on a string of unknown length oscillates as a pendulum with a period of 4.9 s . Parts A to D are independent questions, each referring to the initial situation. Part B What is the period if the string length is doubled? Part C What is the period if the string length is halved? Part D What is the period if the amplitude is doubled? Solution Time period of a pendulum T = 2*pi*sqrt(L/g) part(B) (T2/T1)^2= L2/L1 if L2 = 2*L1 (T2/T1)^2 = 2 T2 = T1*sqrt2 T2 = 4.9*sqrt2 time period T2 = 6.9 s
  • 2. ====================== part C if L2 = L1/2 (T2/T1)^2 = 1/2 T2 = T1/sqrt2 T2 = 4.9/sqrt2 = 4.9/1.41 T2 = 3.5 s ============================== part D time period is independent of amplitude time period remains same 4.9 s