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Grade: upto college level
        A particle having mass 10 g oscillates according to the equation x = (2.0 cm) sin[(100 s-1)t + π/6]. Find (a) the amplitude, the time period and the spring constant (b) the position, the velocity and the acceleration at t = 0.
5 years ago

Answers : (1)

Deepak Patra
askIITians Faculty
471 Points
							Sol. x = (2.0cm)sin [(100s–1) t + (π/6)]
m = 10g.
a) Amplitude = 2cm.
ω = 100 sec–1
∴ T = 2π/100 = π/50 sec = 0.063 sec.
We know that T = 2π √(m/k) ⇒ T2 = 4π2 × m/k ⇒ k = 4 π2/T2 m
= 105 dyne/cm = 100 N/m.  [because ω = 2π/T = 100 sec-1]

(b) At = 0 
x = 2cm sin (π/6) = 2 × (1/2) = 1 cm. from the mean position.
We know that x = A sin (ωt + ∅)
v = A cos (ωt + ∅)
= 2 × 100 cos (0 + π/6) = 200 × √3/2  = 100 √3 sec-1 = 1.73m/s
c) a = – ω2 x = 1002 × 1 = 100 m/s2

						
5 years ago
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