9.) A 2-kg-object is attached to a spring and undergoes simple harmonic motion.

Question

9.) A 2-kg-object is attached to a spring and undergoes simple harmonic motion. At t = 0, the object starts from rest and 10 cm to the right of equilibrium. If the force constant of the spring is k = 75 N/m, calculate the maximum speed and the maximum acceleration of the object. Find the velocity of the object at t = 5 s. 9.) A 2-kg-object is attached to a spring and undergoes simple harmonic motion. At t = 0, the object starts from rest and 10 cm to the right of equilibrium. If the force constant of the spring is k = 75 N/m, calculate the maximum speed and the maximum acceleration of the object. Find the velocity of the object at t = 5 s. 9.) A 2-kg-object is attached to a spring and undergoes simple harmonic motion. At t = 0, the object starts from rest and 10 cm to the right of equilibrium. If the force constant of the spring is k = 75 N/m, calculate the maximum speed and the maximum acceleration of the object. Find the velocity of the object at t = 5 s.

Explanation / Answer

here,

mass of the object , m = 2 kg

k = 75 N/m

maximum displacement , A = 0.1 m

let the maximum velocity be vmax

using conservation of energy

0.5 * k * A^2 = 0.5 * m * v^2

75* 0.1^2 = 2 * v^2

v = 0.61 m/s

angular speed , w = sqrt( K/m)

w = 6.12 rad/s

the maximum accelration , a = A*w^2

a = 3.75 m/s^2

the maximum accelration is 3.75 m/s^2

x(t) = A* sin(w*t)

then

v(t) = A* w * cos(w*t)

at t = 5 s

v(5) = 0.1 * 6.12 * cos( 6.12 * 5)

v(5) = 0.42 m/s

the velocity at t = 5 s is 0.42 m/s

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