Statics

PREFLIGHT

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The following questions refer to the material you were to read in preparation for the lesson.

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Mass on a Horizontal Spring

Consider a mass on a frictionless horizontal surface. Connect a spring to it and set the system into motion and it will oscillate back and forth. Which of the following statements is false?Start
The force vector points in the opposite direction as the displacement vector
The force vector points in the same direction as the velocity.
The force vector points in the same direction as the acceleration
The length (magnitude) of the force vector is proportional to displacement.
Other (please explain below)

Energy in SHM

Conservation of mechanical energy applies to a simple harmonic motion system. The spring potential (1/2 kx²) is red, and kinetic (1/2 mv²) is blue. Start

Graphs of potential and kinetic energy as a function of time show which of the following is true:
The sum of the potential and kinetic energies is constant
The kinetic energy goes through two complete oscillation for each position oscillation.
The spring potential energy goes through two complete oscillations for each position oscillation.
The energy vs time curve is the same functional shape as the energy vs distance curve.
Other (please explain below)
that the total energy is constant, and that energies go through two complete cycles for each oscillation of the object.

honors extra

Dissecting the SHO

Our general equation for position in SHM is:
x(t) = A cos(wt + d)
Let's take this equation apart to analyze each piece separately.
Start

Different:

Answer the following questions:

Change the amplitude of the oscillation

A key characteristic of simple harmonic motion is the relation between oscillation frequency and amplitude. If two equal masses connected to identical springs are released from rest at different points will they have the same angular frequency?

Change the frequency of oscillation

For a spring-mass system, changing the frequency means changing the ratio k/m, because w = (k/m)^�. If we kept the k's the same but doubled one mass, by what factor would the frequency change?

Change the phase

If we only change the phase, what changes in the two graphs of x(t)?

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