A block of mass m = 2 kg is attached to a spring with a spring constant k. The position of the block as function of time is given by: x(t) = 0.2 cos(10t + π/2). Deduce the spring constant, k, and the total energy of the system: Ok = 150 N/m and E = 3 J Ok = 200 N/m and E = 20 J O k = 150 N/m and E = 15 J Ok = 200 N/m and E = 4 J

A horizontal spring attached to a wall has a force constant of k = 830 N/m. A block of mass m = 1.40 kg is attached to the spring and rests on a frictionless, horizontal surface as in the figure below. wiwwwww. x= 0 x = x;/2 x= X; (a) The block is pulled to a position x; = 6.60 cm from equilibrium and released. Find the potential energy stored in the spring when the block is 6.60 cm from equilibrium. 2.91*10**- >X Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. J (b) Find the speed of the block as it passes through the equilibrium position. 6.45 Your response differs from the correct answer by more than 100%. m/s (c) What is the speed of the block when it is at a position x/2 3.30 cm? 5.58 Your response differs from the correct answer by more than 100%. m/s

A pendulum consisting of a particle of mass m supported by a light cord of length L is released from a position ho measured from the lowest position, as shown in the figure below. The cord hits a small peg P located at a distance L/2 vertically below the upper end of the pendulum. T ho m Ohz ho g How high will the mass swing afterwards? hint: consider the conservation of energy in the system. h = ho 12 h=2 ho L h

A marble with a mass of 0.085 kg compresses a spring 5.1 cm. If the spring has a constant k = 150 N/m, what will the velocity of the marble be when it's released?

If a spring is stretched 2.2 cm by a suspended object having a mass of 0.40 kg, what is the force constant of the spring? How much work is done by the spring on the object as it stretches through this distance? Evaluate the work done by the gravitational force on the object (in J).

An archer pulls her bowstring back 0.390 m by exerting a force that increases uniformly from zero to 235 N. (a) What is the equivalent spring constant of the bow? N/m (b) How much work does the archer do in pulling the bow?

A spring is stretched 35.2 cm beyond its equilibrium length. How much energy has been transferred to the spring, if the spring constant is 32.6 N/cm? [Note the units!] E = _J

answer part b

A 2.0 kg object is acted upon by a spring force characterized by the function F=-6x, (this means k = -6N/m).  The speed of the object at x=3.0 m is 8.0 m/s.  Determine the positive value for x where the speed of the object will be 4.9 m/s.  Hint:  The work done between values of x will be 1/2kx22-1/2kx12.  Set this equal to the change in kinetic energy associated with the change in speed.

An object with mass moves with position function r(t) a sin t i + b cos tj + ct k 0 < t < pi /2. Find the work done on the object during this time period.