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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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
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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