Question

A mass of 5 kg stretches a spring 20 cm. The mass is acted on by an external force of 10 sin(t/8) N (newtons) and moves in a medium that imparts a viscous force of 6 N when the speed of the mass is 2 cm/s. If the mass is set in motion from its equilibrium position with an initial velocity of 7 cm/s, formulate the initial value problem describing the motion of the mass. (Use g = 9.8 m/s^2 for the acceleration due to gravity. Let u(t), measured positive downward, denote the displacement in meters of the mass from its equilibrium position at time t seconds. Use up for u' and upp for u''.) u(0) = ____m, u'(0) = ___m/s

          A mass of 5 kg stretches a spring 20 cm. The mass is acted on by an external force of 10 sin(t/8) N (newtons) and moves in a medium that imparts a viscous force of 6 N when the speed of the mass is 2 cm/s. If the mass is set in motion from its equilibrium position with an initial velocity of 7 cm/s, formulate the initial value problem describing the motion of the mass. (Use g = 9.8 m/s^2 for the acceleration due to gravity. Let u(t), measured positive downward, denote the displacement in meters of the mass from its equilibrium position at time t seconds. Use up for u' and upp for u''.)

u(0) = ____m,
u'(0) = ___m/s
        
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Added by Aimee C.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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A mass of 5 kg stretches a spring 20 cm. The mass is acted on by an external force of 10 sin(t/8) N (newtons) and moves in a medium that imparts a viscous force of 6 N when the speed of the mass is 2 cm/s. If the mass is set in motion from its equilibrium position with an initial velocity of 7 cm/s, formulate the initial value problem describing the motion of the mass. (Use g = 9.8 m/s^2 for the acceleration due to gravity. Let u(t), measured positive downward, denote the displacement in meters of the mass from its equilibrium position at time t seconds. Use up for u' and upp for u''.) u(0) = ____m, u'(0) = ___m/s
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Transcript

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00:01 Now here we will be using the mk s system of the spring constant so using mk s system of spring constant k which is the spring constant we will be having k is equal to 5 times 9 .8 over 0 .2 so that is equal to 245...
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