Solve please A spring with a mass of 2 kg has damping constant 12, and a force o

Question

Solve please

A spring with a mass of 2 kg has damping constant 12, and a force of 8.75 N is required to keep the spring stretched 0.5 m beyond its natural length. The spring is stretched 2 m beyond its natural length and then released with zero velocity. Find the position of the mass at any time t. x(t) = A series circuit contains a resistor with R = 120 Ohm, an inductor with L = 10 H, a capacitor with C = 0.001 F, and a 12 V battery. The initial charge is Q = 0.002 C and the initial current is 0. Find the charge and current at time t. Q(t) = I(t) =

Explanation / Answer

1)8.75 = k *0.5

k = 17.5 N/m

2 d2x/dt2 + 12 dx/dt + 17.5 x(t)= 0

solution of this equation is

t = 0 ;x =2 ; dx/dt =0

2) iR + Ldi/dt + idt/C = V

(120i(t) +10 (di/dt) + int_{-infty}^{t}idt/0.001 = 12)

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