A mass m = 4.8 kg is at the end of a horizontal spring of spring constant k = 18

Question

A mass m = 4.8 kg is at the end of a horizontal spring of spring constant k = 180 N/m on a frictionless horizontal surface. The block is pulled, stretching the spring a distance A = 2.5 cm from equilibrium, and released from rest. (a) Write an equation for the angular frequency omega of the oscillation. (b) Calculate the angular frequency omega of the oscillation in rad/seconds. (c) Write an equation for the period T of the oscillations. (d) Calculate the period T of the oscillations in seconds. (e) Write an equation for the maximum speed v_max of the block. (f) Write an equation for the maximum acceleration a_max of the block.

Explanation / Answer

(a)

w = sqrt(k / m)

(b)

w = sqrt(180 / 4.8) = 6.12 rad/s

(c)

T = 2 pi / w = 2 pi * sqrt(m / k)

(d)

T = 2*pi / 6.12

T = 1.025 s

(e)

From energy conservation,

(1/2) k A^2 = (1/2)m * vmax^2

vmax = sqrt(k / m) * A

(f)

F = kx = m*amax

kA = m*amax

so, amax = k * A / m

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