# A force of 8 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring, and the system isthen immersed in a medium that offers a damping force numerically equal to 0.8 times the instantaneous velocity.(a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above theequilibrium position.x(t)ft

Question
109 views help_outlineImage TranscriptioncloseA force of 8 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 0.8 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. x(t) ft fullscreen
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Step 1

Let m be the mass attached and k is the string constant and let β be the positive damping constant. The newton second law for the system is: help_outlineImage Transcriptionclosed x ,dx т dt where x () is the displacement from equilibrium position dt therefore, d x k 0 dr т at т fullscreen
Step 2

Now, find the equation of motion. First, convert the weight into unit of masses:

Step 3

Now, find spring c...

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