Mass on a Spring: A 1.5-kg cart attached to an ideal spring with a force constant (spring constant) of 20 N/m oscillates on a horizontal, frictionless track. At time t = 0.00 s, the cart is released from rest at position x = 10 cm from the equilibrium position.(a) What is the frequency of the oscillations of the cart?(b) Determine the maximum speed of the cart. Where does the maximum speed occur?(c) Find the maximum acceleration of the mass. Where does the maximum acceleration occur?(d) How much total energy does this oscillating system contain?(e) Express the displacement as a function of time using a cosine function.
What will be an ideal response?
(a) 0.58 Hz (b) 0.37 m/s, at the equilibrium position (c) 1.3 m/s2, at maximum displacement (d) 0.10 J (e) x = (0.10 m) cos (3.7 s-1 t)
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Phase Angles: A 50-? resistor is placed in series with a 40-mH inductor. At what frequency will the current in this circuit lag the applied voltage by exactly 45°?
Fill in the blank(s) with the appropriate word(s).
A very long string is tied to a rigid wall at one end while the other end is attached to a simple harmonic oscillator. Which of the following can be changed by changing the frequency of the oscillator?
a. The speed of the waves traveling along the string. b. The tension in the string. c. The wavelength of the waves on the string. d. All of the above. e. None of the above.
Refracting Telescope: A student constructs an astronomical telescope with a magnification of 10. If the telescope has an objective lens of focal length 0.50 m, what is the resulting length of the telescope?
A. 53 cm B. 55 cm C. 60 cm D. 75 cm
A harmonic wave travels with a speed of 200 m/s and has a wavelength of 0.800 m. What is the frequency of the wave?
A) 25.0 Hz B) 40.0 Hz C) 125 Hz D) 80.0 Hz E) 250 Hz