IFHW17

Computer Intensive Physics 211Spring, 1998
InfoMall Homework #17 -Printed only (10 points)
IFHW17:

p.1 of 1
Due 3/12/98

1. (4 pts) Using equations you find on the InfoMall, analyze the results of the activities today. (a)Do the period and frequency you measured for the oscillating mass in MBL17 agree with
theoretical predictions for the spring constant (k) you measured and the mass you used? (b)What was the length of the pendulum in the video?
(c)The mass-on-2-springs in the video presents a slightly more complicated situation. Draw a
Free Body Diagram for two different positions. If each of the two springs had the same
spring constant (k), what is the net force on the puck when it is displaced from equilibrium
by a distance x(in terms of kand x)? What is the effective spring constant (i.e. what would
the constant of ONE spring have to be in order to provide the force due to these TWO
springs)? Predict the oscillation frequency for the puck, in terms of kand its mass m. What
was the ratio k/mfor the puck-spring system in the video?

2. (2 pts) Simple Harmonic Motion is a consequence of a restoring force whose magnitude is proportional to distance from equilibrium. The Differential Equation describing the motion is relatively simple to derive.
(a)Write Hooke's Law, the equation describing the force due to a spring. This is a restoring
force whose magnitude is proportional to distance from equilibrium.
(b)Use Newton's Second Law to write an expression for the acceleration of an object attached to
a spring in terms of the distance from equilibrium.
(c)Now, replace the "a" for acceleration with the definition for acceleration in terms of
derivatives of position.
(d)Write the general solution for this differential equation (Find it in the Infomall or use Maple).
It should look familiar! (Note: how is the function related to its second derivative?}

3. (4 pts) A 2.0-kg mass is attached to a spring with a force constant of 98 N/m. The mass is resting on a frictionless horizontal plane in a position such that the spring applies a horizontal force of 9.8 N to the mass, and it is then released.
(a)What is the amplitude of SHM?
(b)What is its period?
(c)Where during the motion is the maximum potential energy stored in the spring?
(d)What is the value of the maximum potential energy stored in the spring?
(e)Where during the motion is the kinetic energy of the mass at its maximum value? (g)What is the value of the maximum kinetic energy of the mass?
(h)What is the maximum velocity of the vibrating mass?
(i)What are the values of the potential, kinetic, and total energies of the motion when the mass
is 2 cm from its equilibrium position?



		Computer Intensive Physics 211Spring, 1998 InfoMall Homework #17 -Printed only (10 points) IFHW17:		p.1 of 1 Due 3/12/98
		1. (4 pts) Using equations you find on the InfoMall, analyze the results of the activities today. (a)Do the period and frequency you measured for the oscillating mass in MBL17 agree with theoretical predictions for the spring constant (k) you measured and the mass you used? (b)What was the length of the pendulum in the video? (c)The mass-on-2-springs in the video presents a slightly more complicated situation. Draw a Free Body Diagram for two different positions. If each of the two springs had the same spring constant (k), what is the net force on the puck when it is displaced from equilibrium by a distance x(in terms of kand x)? What is the effective spring constant (i.e. what would the constant of ONE spring have to be in order to provide the force due to these TWO springs)? Predict the oscillation frequency for the puck, in terms of kand its mass m. What was the ratio k/mfor the puck-spring system in the video?
		2. (2 pts) Simple Harmonic Motion is a consequence of a restoring force whose magnitude is proportional to distance from equilibrium. The Differential Equation describing the motion is relatively simple to derive. (a)Write Hooke's Law, the equation describing the force due to a spring. This is a restoring force whose magnitude is proportional to distance from equilibrium. (b)Use Newton's Second Law to write an expression for the acceleration of an object attached to a spring in terms of the distance from equilibrium. (c)Now, replace the "a" for acceleration with the definition for acceleration in terms of derivatives of position. (d)Write the general solution for this differential equation (Find it in the Infomall or use Maple). It should look familiar! (Note: how is the function related to its second derivative?}
		3. (4 pts) A 2.0-kg mass is attached to a spring with a force constant of 98 N/m. The mass is resting on a frictionless horizontal plane in a position such that the spring applies a horizontal force of 9.8 N to the mass, and it is then released. (a)What is the amplitude of SHM? (b)What is its period? (c)Where during the motion is the maximum potential energy stored in the spring? (d)What is the value of the maximum potential energy stored in the spring? (e)Where during the motion is the kinetic energy of the mass at its maximum value? (g)What is the value of the maximum kinetic energy of the mass? (h)What is the maximum velocity of the vibrating mass? (i)What are the values of the potential, kinetic, and total energies of the motion when the mass is 2 cm from its equilibrium position?