10.1.3 Energy in Simple Harmonic Motion Flashcards
Energy in Simple Harmonic Motion
- For a mass on a spring moving in simple harmonic motion, the total energy of the system is the sum of the potential energy of the spring and the kinetic energy of the mass. As the mass oscillates, the total energy remains constant, but the relative amounts of kinetic and potential energy change.
- Energy considerations are often a convenient tool for analyzing SHM. Energy conservation, for example, can be used to derive the speed of an object in SHM as a function of position:
A mass m connected to an ideal spring with spring constant k is executing simple harmonic motion on a horizontal frictionless surface. The position of the mass is given by x(t) + Acoswt. Which of the following is true when the kinetic energy of the system is equal tot he potential energy of the system?
tan^2 wt = 1
A woman shopping for her next home-improvement project loads her 1.00 × 103 kg car with 250.0 kg of materials. The springs on the car compress 3.10 cm. When the car hits a bump, the springs are compressed an additional 5.00 cm and the car and its occupants begin SHM. Which of the following is the vertical component of the springs’ velocity as they pass through-2.00 cm?
0.815 m / s
A spring with a spring constant of 200 N / m is stretched to 25.0 cm and allowed to oscillate with an attached mass at a frequency of 3 Hz. When x = 2.5 cm, which of the following is the total energy?
6.25 J
A mass (m = 2.5kg) connected to a spring (k = 1.9 N/m) starts in equilibrium at x = 0 and is free to slide horizontally on a frictionless surface. The mass is given a brief impulse that sends it in the positive x-direction. If the velocity of the mass at x = 0.47 m is 0.37 m/s, what is the maximum x-value is reaches?
0.63 m
A mass on a spring oscillates around an equilibrium point at x=0 in simple harmonic motion. Neglecting friction, which of the following functions describes its kinetic energy as a function of position? A and B are positive constants.
K = A - Bx^2
As a 5.00 kg mass passes through x = −0.50 m while executing SHM on a spring with
k = 250.0 N / m. As it passes, the mass has a velocity of 3.95 m / s. Which of the following is the amplitude?
0.75 m
A certain mass-spring system executing simple harmonic motion has a total energy E. The system is brought to rest and restarted in simple harmonic motion so that the speed of the mass at the equilibrium point x = 0 is twice as large as before. What is the total energy of the new system?
4E
Which of the following is true?
Position is a minimum when velocity is a maximum.
A particle is oscillating between y = −3.21 m and y = −3.27 m in simple harmonic motion with a period of 0.25 s. How fast is it moving when it is at the position y = −3.26 m?
0.56 m / s
