Show Intro/Instruct m -5-in a medium that exerts a resistive force with magnitude proportional to the...
A mass of 1.25kg stretches a spring 0.05m. The mass is in a medium that exerts a viscous resistance of 192N when the mass has a velocity of 6m/s. The viscous resistance is proportional to the speed of the object. Suppose the object is displaced an additional 0.06m and released. Find a function u(t) to express the object's displacement from the spring's natural position, in m after t seconds. Let positive displacements indicate a stretched spring, and use 9.8m/s^2 as...
Differential Equation problem A mass of 0.25kg stretches a spring 0.1m. The mass is in a medium that exerts a viscous resistance of 14N when the mass has a velocity of 4m/s. The viscous resistance is proportional to the speed of the object. Suppose the object is displaced an additional 0.08m and released. Find a function u(t) to express the object's displacement from the spring's natural position, in m after t seconds. Let positive displacements indicate a stretched spring, and...
helpful formulas: mu’’(t)+cu’(t)+ku(t)=0 m is the mass c is the damping coefficiant k is spring constant Fd=cu’(t) k=mg/(spring displacement) A mass of 1.5 kg stretches a spring 0.08 m. The mass is in a medium that exerts a viscous resistance of 25 N when the mass has a velocity of 2 m. The viscous resistance is proportional to the speed of the object. Suppose the object is displaced an additional 0.03 m and released. Find an function to express the...
Solving variation problem 5. Let a be directly proportional to m and n2, and inversely proportional to y3. If a9 when m 4,n-9, and y - 3, find a when m-6,n2, and y -5. 7. Current Flow In electric current flow, it is found that the resistance offered by a fixed length of wire of a given material varies inversely as the square of the diameter of the wire. If a wire 0.01 in. in diameter has a resistance of...
this is differential equations practice problem part d should be t = 0, thank you in sdvancdd! 1. An object of mass m is fired vertically upward with an initial speed of vo. Suppose the air resistance is proportional to the square of velocity. Let k > O be the constant of proportionality. Use g as the acceleration due to gravity. Let v(t) be the velocity at time t. a) Write down the differential equation in effect for v(t) until...
5. (15 pts] A force acting on an object is proportional to the square root of the distance the object moves. The equation for the distance r is: 19 = kyr, for some constant k. The object starts at t=0 with position r = 0 and velocity v = 0. The object moves four meters in the first second. That is, r(t = 1) = 4. (a) Find the object's velocity as a function of position, v(r). (b) Find the...
If a single constant force acts on an object that moves on a straight line, the object's velocity is a linear function of time. The equation v=vi + at gives its velocity v as a function of time, where a is its constant acceleration. What if velocity is instead a linear function of position? Assume that as a particular object moves through a resistive medium, its speed decreases as described by the equation v = vi-vx, where k is a...
NOTES: HI, PLEASE SOLVE BY USING ANALYTICAL METHOD WHICH IS RELATED TO FLUID MECHANICS(DRAG FORCE).TQ 25.19 Assuming that drag is proportional to the square of velocity, we can model the velocity of a falling object like a parachutist with the following differential equation: dv dt where v is velocity (m/s), 1 = time (s), g is the acceleration due to gravity (9.81 m/s), c = a second-order drag coefficient (kg/m). and m 90-kg object with a drag coefficient of 0.225...
Q.3) (7 Marks An object of mass m is being acted upon by a force F(x) = Fosin (cx), where F. = 2 N and c = 0.5 rad/m are constants (a) Prove that this force is conservative. (b) Find the potential energy function V(x) (c) Make a graph of the potential energy V(x) as a functions of x in the interval [x = -a m,x = + m) d) Us previous graph to discuss the motion of the particle...
Problem 36 bclow presents a model describing the drag of a fluid medium that is released from rest at time t 0 (same initial conditions). Using Newton's Second Law, you build a model of the form particle moving through a (governing equation (initial velocity) mi mg-F drag '0 (0)(0)a (t) is the particle's position, m is the mass of the particle, g is the acceleration due to gravity, and Fa is the magnitude of the drag force. You account for...