Assume the motion of a mass-spring system with damping is governed by d²x dx +b 1 +16x = 0; x(0)=;, x'(0)= 0. 2' di? dt Find the equation of motion and sketch the graph for the three cases where b= 4, 8, and

Q: JA spring with a spring constant k of 100 pounds per foot is loaded with 1-pound weight and brought…

A: We have given that: Spring constant, k = 100 lb/ft Weight, W = 1 lb Initial speed = 0 ft/s Initial…

Q: 4) Solve: x.[dy/dx] - y = x²sinx (Hint: Use the integrating factor).

A: Step 1: Step 2: Step 3: Step 4:

Q: If the foundation of a structure with a degree of freedom is affected by displacement with the…

A: Given:- U g(t)=10 sin (30t)

Q: 3. Write the exact differential: f(x,y)=e-y-el-

A: Given- fx,y=ex-y-ey-x To write the exact differential.

Q: d sec*t dt dx.

A:

Q: A 7 kg weight is attached to a spring with constant k = 63 kg/m and subjected to an external force…

A: I have explained everything with in the solution. Please go through that.

Q: Assume that y = 5x and dx/dt = 2. Find dy/dt.

A: Consider y = 5xApplying derivative with respect to t on both sides and plugging the values:

Q: Solve the equation xcosy dy+(x+2)siny dx=0.

A:

Q: 7. Find an equation of the line tangent to the curve y = 3x² – 1 and perpendicular to the line x

A:

Q: x +y-y° =5

A: The given equation is x2+y-y3=5 We have to find dydx=?

Q: Copy the slope fields (mentioned in the Attachment) and sketch in some of the solution curves. y' =…

A: Given: y'=y(y+1)(y-1)

Q: y = In(x +1)

A: Given that : y = ln(x2 + 1). Find dy/dx  We know that derivative of - d(lnx)/dx = 1/x. And d(xn)/dx=…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.