Mechanical Oscillation

Pre$-$lab questions: Answer these questions and submit your answers via Blackboard before coming to lab. Make sure your submission is correctly uploaded to Blackboard and readable. If your submission is not loaded properly or if it is not readable, you will receive no credit for your submission.

Based on your reading, what do the terms periodic motion and harmonic motion mean? Explain each term using one or two complete sentences.

Remember how a spring works: when you pull on it$,$ it stretches. Newton's $3^{rd}$ Law of motion says that the spring pulls back on you too. If you pull the end of the spring in the $+x$ direction with a force, vec$(F),$ in the $+x$ direction, the spring stretches by an amount $x.$ You know that the force has only an $x$ component, and hence

$F_x=kx$

where $F_x$ is the force applied, $k$ is the force constant of the spring, and $x$ is how much the spring stretches.

$($a$)$ What are the physical dimensions of the force constant, $k?$

$($b$)$ What does Newton's $3^{rd}$ Law say about the force that the spring must exert on the hand stretching it$?($In one dimension you can use $+-$ to show direction.$)$

$3.$ From your reading, if a mass, $m,$ is attached to a spring of force constant $k$ to make an oscillator, what formula gives the period of oscillation, $T?$

$4.$ If the mass is released from rest at a negative displacement, sketch a graph of the displacement vs$.$ time for the subsequent motion as a function of time for the interval $0.$ Draw $iton$ the displacement axes $to$ the right.

$5.$ From the displacement$-$time graph you sketched, sketch the velocity$-$time and acceleration$-$time graphs $on$ the axes provided. When $is$ velocity $0?$ When $isit$ a maximum? When $is$ the acceleration $0?$ When $isit$ a maximum? Are the velocity and acceleration ever $0at$ the same time?

$6.$ From the acceleration$-$time graph, sketch the force$-$time graph. Comparing the force$-$time graph $to$ the displacementtime graph, how are they similar? How are they different? $Is$ the force ever $0?Ifso,at$ what point $in$ the motion? Why doesn't the mass just stop there $if$ the force $is0?$

$14-3$