5. A block is attached to a horizontal spring. Find a model for the displacement d as a function of time given the following conditions: a. At time t = 0, the block is pulled to the left 6 cm with a frequency of 2 Hz.

One end of a horizontal rope is attached to a prong of an electrically driven tuning fork that vibrates at 150 HzHz . The other end passes over a pulley and supports a 2.50 kgkg mass. The linear mass density of the rope is 0.070 kg/mkg/m . For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Mineral samples in a mine shaft. 1.What is the speed of a transverse wave on the rope? Express your answer in meters per second.   2.What is the wavelength? Express your answer in meters.   3.How would your answers to part (A) change if the mass were increased to 5.00 kgkg ? Express your answer in meters per second.   4.How would your answers to part (B) change if the mass were increased to 5.00 kgkg ? Express your answer in meters.

A mass of 0.407 kilograms is oscillating horizontally on a spring. Its position is given by the equation x = [0.108 sin (9.24t + 0.82) + 0.683] m. a. What is the spring constant of the spring? Include units in your answer. More information. b. The velocity of the mass is another sinusoid, which also can be modeled using the equation v = [A sin (Bt + C) + D] m/s. What are those values? Do not bother with units.A:  B:  C:   (between 0 and 2?)D:  c. The acceleration of the mass is yet another sinusoid, which again can be modeled using the equation a = [A sin (Bt + C) + D] m/s/s. What are those values of A and C? Do not bother with units. Hint: For A, consider Newton's second law of motion.A:  C:   (between 0 and 2?)Note that the values of B and D for the acceleration equation are the same as the values of B and D for the velocity equation.

a. If you took a pendulum to the moon where g = 1.6 m/s2, what change would you observe in its period? b. Are there factors other than length and gravitational acceleration that affect the period of the pendulum? Why is the period of a pendulum bob independent of its mass?

A mass of 2.00kg is pulled to the right 15.5 cm and released at t=0 seconds.  The period of the oscillation on a frictionless surface is measured to be 2.05 seconds. a. what is the spring constent? b. what is the maximum velocity? c. what is the maximum acceleration?

A mass (100 g) rests on a second mass (850 g) that is attached to a spring with k = 75.0 N/m.  The coefficient of static friction between the two mass is 0.70.  The masses are set into motion that is simple harmonic on a frictionless surface.  a. What is the maximum amplitude the oscillation can have without the masses slipping against each other? b. What is the speed of the masses when they pass through the equilibrium position for the amplitude computed in part a?

A mass m = 3.3 kg is at the end of a horizontal spring on a frictionless horizontal surface. The mass is oscillating with an amplitude A = 4.5 cm and a frequency f = 1.5 Hz. a. Write an equation for the spring constant k.  b. Calculate the spring constant k, in Newtons per meter.  c. Write an equation for the total mechanical energy, E, of the motion. Your expression should be in terms of the variables in the original problem statement.  d. Calculate the total mechanical energy E, in joules.

4. The displacement y(t) of an undamped oscillator of mass m>0 on a spring with spring constant k>0, and initial displacement a + 0 and initial velocity zero satisfies my" + ky = 0, y(0) = a, y'(0) = 0 %3D a. Solve this initial value problem. b. Show that the solution is periodic with period T, meaning that y(t+T)= y(t), and express Tin terms of m and k.

A mass of 240 g oscillates on a horizontal frictionless surface at a frequency of 2.5 Hz.   a. What is the effective spring constant for this motion?

5. A "seconds pendulum" is one that moves through its equilibrium position once each second. (The period of the pendulum is precisely 2 s.) The length of a seconds pendulum is 0.992 7 m at Tokyo, Japan and 0.994 2 m at Cambridge, England. What is the ratio of the free-fall accelerations at these two locations?