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A 2-kg mass is attached to a spring with stiffness 40 N/m. The damping constant for the system is 815 N-sec/m. If the mass is pulled 10 cm to the right of equilibrium and given an initial rightward velocity of 2 m/sec, what is the maximum displacement from equilibrium that it will attain?

$$t_{n+1}=\approx .182$$

05:23

Karee N.

Calculus 2 / BC

Chapter 4

Linear Second-Order Equations

Section 9

A Closer Look at Free Mechanical Vibrations

Differential Equations

Missouri State University

Oregon State University

Harvey Mudd College

Boston College

Lectures

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problem number nine Using the expression and avoidable dash plus B y Nash plus key why is equal to zero so em is equal to two. B is equal to 80 spoke square root off fire K is equal toe 40. So why nobody is equal to 1/10. Why Dash node is equal to two so to wider will dash plus eight square root off five y dash plus 40 y is equal to zero. Ah, let's why is equal toe e over r a. Poor Artie so e four rt so e for rt. Times two R squared plus eight square root file are plus 40 is equal to zero, so are is able to a negative ah to square root or five eso. Why is equal to see one paper negative two square five t plus C toe T people Negative to a square root five things So why dash is equal to a negative to square root or fine. See one people on anything to square root. Five. Teen plus I see two people are negative through square root five T minus ah to square root for five C to T people Negative two square root for five using why. Note AH t is equal to zero or industry is equal to one over things, so 1/10 is ableto see one and two is equal to negative square root 5/5 plus C two, so C two is equal to toe plus square. Root for five over over five. To get the maximum displacement we must find when y nash is equal to zero, so zero is equal to two ive or negative two square root for five T minus four square root or five plus two. T people are negative two square root or five teams so using in yet in method. Ah, you say that T n plus one is equal to TN minus. F off tiene over f dash or off tiene ah, in this case, if 50 n is equal to two people or negative two. Square root file. A T minus four square root off five plus two T people are negative. Two square root for five team and if dash off T is equal to negative. Four a square root of five a square root for five. Teen plus 40 plus four square root or fire ah t e power Negative two square root for five T minus four square root five plus to paper negative to a square root for 55 Now we big starting point for the end, which is open to second, so the end plus one is equal toe opening to minus two people. A negative to a square root of fire team minus for a square root fire, plus two times all point to a poor negative. Two square root for five times over into over and negative four square root file in power Negative two square root off five times opening to plus 14 plus four square root off five. Time is opening to keep our negative two square room on fire. Ah, open to minus four square root five plus two he or negative two square root off five times opening to, ah, the final answer that is opening to minus negative. Opening to go 778 over. Negative 4.12884 which approximately equal 1.82

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