Question

84
COMPLEMENTARY PHYSICS
PROBLEMS
1. A particle executes simple harmonic motion along a straight path of
length 30 cm with time period 3s. What is the time required for the particle
to move between two points 7cm on either side of the mean position?​

Answer 1

Answer:

given, amplitude, A = 25cm

time period, T = 3sec

so, equation of particle executing SHM, y = Asin(2πt/T)

= (25cm)sin(2πt/3 )

we have to find the time required for the particle to move between two points 12.5 cm on either side of the mean position.

so, distance travelled by particle from one point to mean position, y = 12. 5cm

now, y = 12.5cm = (25cm)sin(2πt/3)

⇒1/2 = sin(π/6) = sin(2πt/3)

⇒π/6 = 2πt/3

⇒t = 1/4 sec

similarly, time taken to travel by particle from mean to other point , t = 1/4 sec

so, total time required , t' = 2t = 2 × 1/4 sec = 1/2 sec

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