A mass of 4kg stretches spring 40 cm. The mass ls acted on by an external force of 180e-2t+196N and moves in a medium that imparts a viscous force of 34N when the speed of the mass is 1/3 m/sec. Mass Is set in motion from equilibrium position with an initial velocity of 1 m/sec: A) Formulate an initial value problem (IVP) B) Solve the IVP C) Identify end behavior of the entire solution.

4. Certain frictional forces have magnitude proportional to the square of the velocity of the moving object. Thus |Ffriction| = -yv² for some positive constant y. Here there is an annoying sign issue since the frictional force must have sign opposite to the velocity. One can write Felastic = -y|v|v. If an object of mass m is subject to this frictional force and no other forces, and the initial velocity is positive, then the velocity will always be positive and we can just say Ffriction Then the position y of the particle satisfies the equation -yo?. dy dt2 2 dy +y dt = 0. Write out a solution of this equation for the initial conditions y(0) = Yo, (dy/dt)(0) the substitution u = = vo. Hint: The equation reduces to first order. Use dy/dt and solve the first order equation to get u. Then integrate u to get y.

Calculate the force (in N) a piano tuner applies to stretch a steel piano wire 7.30 mm, if the wire is originally 0.860 mm in diameter and 1.35 m long. Young's modulus for steel is 210 x 109 N/m2. (No Response)N

Please answer and solve the question correctly. Thank you!!