A mass of 6 kg stretches a spring 24 cm. The mass is acted on by an external force of 5 sin() N (newtons) and moves in a medium that imparts a viscous force of 12 N when the speed of the mass is 4 cm/s. If the mass is set in motion from its equilibrium position with an initial velocity of 10 cm/s, formulate the initial value problem describing the motion of the mass. Assume that g = 9.8 m 6 +12 +2.45u Ssin( () 10 6 +300+245u=5sin( (). 10 6u" + 300u +245u Ssin( 6u" + 300u' +2.45u = 5sin() 6 + 12 +245u = 5sin(). (0) = 0, / (0) = 0.10, (0) = 0.10, 1/(0) = 0. uin meters. uin meters. (0) = 0, (0) 0.10, in meters. (0) = 0, / (0) = 0.10, (0) = 0, 1/(0) = 0.10, uin meters. uin meters.

An object with an initial velocity of (0) = 2 has an acceleration of a(t) = 3t² + 6. Find its velocity at t = 5. 신

A particle moves on the 0x axis with acceleration proportional to velocity. Assuming that v(0) = 3, v(1) = 2 and x(0) = 0, determine the position of the particle at time t.

A mass weighing 16 pounds stretches a spring 8 feet. The mass is initially released from rest from a point 4 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a 1 damping force that is numerically equal to - the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 20 cos(3t). (Use g = 32 ft/s2 for the acceleration 2 due to gravity.) x(t) = ft