Real springs have mass. How will the true period and frequency differ from those given by the equations for a mass oscillating on the end of an idealized massless spring?
If a pendulum clock is taken to a mountain top, does it gain or lose time, assuming that it is correct at a lower elevation?
Young and Freedman 13-37:
An apple weighs 1.00N. When you hang it from the end of a long spring of force constant 2.00 N/m and negligible mass, it bounces up and down in SHM. If you stop the bouncing and let the apple swing from side to side through a small angle, the frequency of the motion is half the bounce frequency. What is the unstretched length of the spring?
Young and Freedman 13-26:
A torsion pendulum is a thin disk attached to a stiff wire or thin rod. The disk undergoes SHM if twisted slightly and released. … A thin metal disk of mass 1.00x10-3 kg and radius 0.500 cm is attached at its center to a long fiber. When twisted and released, the disk oscillates with a period of 1.00 s. Find the torsion constant of the fiber. (Reviewing the section on angular SHM on p.405 of the text might be helpful.)
What happens to the period of a playground swing if you rise up from sitting to a standing position?
The frequency with which a dog pants is the natural frequency of their respiratory system. Is this good or bad? Why?
Young and Freedman 13-40:
A connecting rod from a car engine is pivoted about a horizontal knife edge as shown in figure 13-27 on page 421 of the text. The rod has mass 2.00 kg. The center of gravity of the rod was located by balancing and is 0.200 m from the pivot. When it is set into small-amplitude oscillation, the rod makes 100 complete swings in 120 s. Calculate the moment of inertia of the rod about the rotation axis through the pivot.
If time –
Young and Freedman 13-75:
Three positively charged particles are maintained in a straight line. The end particles are identical and are held fixed at a distance 2 R0 apart. The potential energy of the force acting on the center particle can be written as U=A[1/r – 1/(r-2R0)], where A is a constant and r is the distance from the left-hand particle to the center particle. a) Show the force on the center particle is F=A[1/r2 – 1/(r-2R0)2]. b) Show that r=R0 at equilibrium. c) Use r=R0+x and the first two terms of the binomial expansion to show that F=-(4A/R03)x and that the force constant is k=4A/R03. d) What is the frequency of small-amplitude oscillation of the center particle if it has mass m?