A block of mass 680 g is attached to a horizontal spring whose spring constant is 65 Nm^-1 . The block is pulled to a distance of 11 cm from the mean position and released from rest. Calculate :(i) angular frequency, frequency and time period(ii) displacement of the system(iii) maximum speed and acceleration of the system

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2015-10-06T21:55:10+05:30

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M = 0.680 kg
k = 65 N/m
maximum deformation = A = amplitude =  0.11 m

initial potential energy = total energy = KE + PE
   = 1/2 k A²  = 1/2 * 65 * 0.11²  J

angular frequency ω = √(k/m) = √(65/0.680) = 9.77  rad/sec
frequency = f = ω/2π =  1.556 Hz
T = 1/f = 0.642 Sec

Displacement of the system:  x = A Cos (ω t) ,  as  at t=0, x = A.
                       x = 0.11 Cos (9.77 t)  meters

maximum speed = v₀ = A ω = 1.0747  m/s
maximum acceleration = a₀ = A ω² ≈ 10.50 m/s²

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