A block with mass 2 kg is placed on a frictionless, horizontal surface and attac

Question

A block with mass 2 kg is placed on a frictionless, horizontal surface and attached to a spring with stiffness 800 N/m. The other end of the spring is fixed to the wall such that the block is resting at the spring's equilibrium length.

The block is then displaced 10 cm in the positive direction, and at time t = 0 s, the block is released from rest. Give an equation for the position x of the block (in cm) at any time t.

write an equation

A block with mass 2 kg is placed on a frictionless, horizontal surface and attached to a spring with stiffness 800 N/m. The other end of the spring is fixed to the wall such that the block is resting at the spring's equilibrium length of the block The block is then displaced 10 cm in the positive direction, and at time t = 0 s, the block is released from rest. Give an equation for the position (in cm) at any time t w; cm

Explanation / Answer

The equation of a spring - mass system performing simple harmonic motion can be written as-

x(t) = A*cos bt

where A = amplitude = 10 cm (given)

b = sqrt[k / m] = sqrt[800 / 2] = sqrt[400] = 20

so we have the equation of the spring-mass system as -

x(t) = 10*cos(20t)

This is your answer.

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