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A 16 lb weight is suspended from a spring having a spring constant of 5 lb/ft. Assume that an external force given by 24 sin (10t) and a damping force with damping constant 4, are acting on the spring. Initially, the weight is at rest at its equilibrium position. Find the position of the weight at any time. Find the steady-state solution. Find the amplitude, period, and frequency of the steady-state solution. Determine the velocity of the weight at any time.

This from the area of ODE, and I am not aware of these physical terms to form the ODE and solve to get the required parameters. Please help me on this

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    $\begingroup$ I have edited the title, e question kuduthal alkarku helpful aagan :) $\endgroup$
    – Reine Abstraktion
    Apr 30, 2021 at 9:36

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A 16 lb weight is suspended from a spring having a spring constant of 5 lb/ft. Assume that an external force given by 24 sin (10t) and a damping force with damping constant 4, are acting on the spring. Initially, the weight is at rest at its equilibrium position. Find the position of the weight at any time. Find the steady-state solution. Find the amplitude, period, and frequency of the steady-state solution. Determine the velocity of the weight at any time.

A somewhat decent discussion can be found from page-356 of this publicly available pdf, any how the ODE you are looking for is:

$$ m \frac{d^2 x}{dt^2} + b \frac{dx}{dt} + kx=F(t) \tag{1}$$

Where,

$ m =16,k=5,F(t)=24 \sin(10t),b=4$

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