Problems on SHO Energy

S15 A 1.0-kg mass is attached to a spring with a force constant, k = 100 N/m. The spring is stretched by 5.0 cm beyond its equilibrium position and the mass is then released.

a.) Describe in words the subsequent motion of the mass, from when it's released to a time, t = 1.25 seconds. In your description, discuss the position and velocity of the mass at different times using its equilibrium position as a reference. Take positive positions to correspond to stretching the spring.
b.) How much potential energy (PE) does the mass and spring have immediately before the system is set into motion (i.e., the mass is released)?
c.) What is the kinetic energy (KE) of the mass as it passes through the equilibrium position?
d.) What is the spped of the mass as it moves through the equilibrium position?
e.) How much faster would the mass move through the equilibrium position if the spring were twice as stiff (i.e., the force constant of the new spring were 200 N/m) and the spring is still stretched by 5.0 cm before the mass is released?

S16 There are three physical quantities necessary to describe a mass and spring "simple-harmonic oscillator". These are the

the "stiffness" or the force constant (k) of the spring
the magnitude of the mass (M)
the total energy (sum of PE and KE) of the mass and spring

Describe in words and in mathematical equations how these physical quantities are interrelated to quantitative descriptions of the motion, including

the period (T) of the resulting oscillation
the amplitude (y_max) of the oscillation
the speed of the mass as it goes through equilibrium, v_max

Return to P105 Course Schedule

Last updated: 14 Sep 1999Comments: bland@indiana.edu