a. What are the periods of S2 and S3? b. What are the forces on S2 and S3? c. What is the kinetic-energy ratio K1/K3 for S1 and S3?

1 A tank contains 460 gallons of water and 10 oz of salt. Water containing a salt concentration of (1+ -sin t) oz/gal flows into the 2 tank at a rate of 6 gal/min, and the mixture in the tank flows out at the same rate. The long-time behavior of the solution is an oscillation about a certain constant level. What is this level? What is the amplitude of the oscillation? Round the values to two decimal places. Oscillation about a level = i oz Amplitude of the oscillation = i Oz.

A spring has an unstretched length of 10 cm. It exerts a restoring force F when stretched to a length of 11 cm.a. For what total stretched length of the spring is its restoring force 3F?b. At what compressed length is the restoring force 2F?

Q5 (Conical pendulum) A pendulum consists of a light string of length a fixed at O and with a mass m attached to the free end A. The string is held so that OA makes an angle a to the downward vertical and then set in motion so that the mass m undergoes horizontal circular motion. What is the period of this circular motion?

A 10kg mass suspended at a height of 10 meters above a massless platform attached to a vertical spring with a stiffness constant of k = 1000 N/m. Ignore air resistance, and g is 9.8 m/s². You are not required to, but it is always helpful (and nice for me to see) if you make a drawing of the situation. a. When the mass is released it will fall onto the platform. By what length will the spring compress while the mass is in contact with the platform? b. Now consider the situation where the mass starts at the same height but is thrown downwards with an initial speed of 3 meters per second. What will the maximum compression of the spring be in this case? c. Does the answer to b change if the mass was thrown upwards at the same speed instead?

In a science museum, you may have seen a Foucault pendulum, which is used to demonstrate the rotation of the earth. In one museum’s pendulum, the 110 kg bob swings from a 15.8-m-long cable with an amplitude of 5.0°.a. What is the period of this pendulum?b. What is the bob’s maximum speed?c. What is the pendulum’s maximum kinetic energy?d. When the bob is at its maximum displacement, how much higher is it than when it is at its equilibrium position?

Suppose that during each step, the leg of the studen swings through a total distance of 2.0 m. At the end of the swing, this foot rests on the ground for 0.2 s before the other leg begins its swing.a. At what speed does this student walk? (Think carefully about how far forward the student moves at each step.)b. The swinging leg reaches its maximum speed at the bottom of its arc. How many times faster is this maximum leg speed (measured with respect to the ground) than the average walking speed?

Item 14 A 0.50 kg mass is attached to a spring with a force constant of 30 N/m and released from rest a distance of 4.0 cm from the equilibrium position of the spring. Part A What is the maximum speed of the mass? Express your answer using two significant figures. ► View Available Hint(s) 17 ΑΣΦ Umax = Submit ? m/s

A crate with mass m is placed above a ramp with an angle 0, and a distance L from a spring with a spring constant k. Suppose that the ramp and crate experience a coefficient of kinetic friction u, solve for the following: a. speed of crate before it compresses the spring b. maximum compression of the spring C. How far does the crate get to its initial distance when it rebounds? Wwwww

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