A $2.0\mathrm{kg}$ block is gently lowered onto a vertical spring, and the spring compresses $5.0\mathrm{cm}.$ Another block is added, and the spring compresses an additional $3.0\mathrm{cm}.$ What is the mass of the second block added?

(II) A wood block of mass 52 g floats on a lake, bobbing up and down at a frequency of 3.5 Hz.

(b) A partially filled water bottle of mass 0.28 kg and almost the same size and shape of the wood block is tossed into the water. At what frequency would you expect the bottle to bob up and down? Assume SHM.

A spring with spring constant 15 N/m hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 6.0 cm and released. If the ball makes 30 oscillations in 20 s, what are its (a) mass and (b) maximum speed?

A chair of mass 30 kg on top of a spring oscillates with a period of 2s. (a) Find the spring's force constant. You place an object on top of the chair, and it now oscillates with a period of 3s. (b) Find the object's mass.

(II) A 1.45-kg mass stretches a vertical spring 0.245 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?

(II) A block of mass m is supported by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 14–31). What will be the frequency of vertical oscillation?

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(III) A uniform 1.25-m-long stick of mass M can rotate easily about a hinge at one end and is held horizontal by a spring with spring constant k attached at the other end (Fig. 14–32). If that end of the stick oscillates up and down slightly, what is its frequency? [Hint: Write a torque equation about the hinge.] <IMAGE>

(II) Estimate the spring constant in a child’s pogo stick if the child has a mass of 32 kg and bounces once every 1.6 seconds.