. a) A simple harmonic oscillator executes motion whose amplitude is 0.20 m and it completes 60 oscillations in 2 minutes. i) Calculate its time period and angular frequency. ii) If the initial phase is 45, write expressions for instantaneous displacement, velocity and acceleration. iii) Also calculate the maximum values of velocity and acceleration of the oscillator.
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A = 0.20 m
T = 120 sec / 60 = 2 sec
angular frequency = ω = 2π/T = π rad/sec
instantaneous displacement x(t) = 0.20 Sin (π t + π/4)
v(t) = dx/dt = 0.20 * π Cos (π t + π/4) m/sec
max velocity = π/5 m/s
a(t) = dv/dt = - 0.20 π² Sin (π t + π/4) m/sec²
max acceleration = π²/5 m/s²
T = 120 sec / 60 = 2 sec
angular frequency = ω = 2π/T = π rad/sec
instantaneous displacement x(t) = 0.20 Sin (π t + π/4)
v(t) = dx/dt = 0.20 * π Cos (π t + π/4) m/sec
max velocity = π/5 m/s
a(t) = dv/dt = - 0.20 π² Sin (π t + π/4) m/sec²
max acceleration = π²/5 m/s²
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