Using Models of SHM

Question 1

What is the formula for acceleration of all simple harmonic oscillations?

Answer 1

a=-4 pi ^2f^2*x

or a=-w^2x where w is the angular frequency.

Question 2

What is acceleration of a mass oscillating on a spring of spring constant k?
Which equation can be derived from combining a=-4pi^2f^2*x and this equation?

Answer 2

a=-kx/m

T=2pi*(m/k)^1/2

Question 3

When mass increases, what is the effect for the time period of a mass-spring oscillator?

Answer 3

Time period also increases.

Question 4

What is the experiment for measuring the time period of a mass on a spring?

Answer 4

Linking 3-4 masses will reduce stiffness of springs in series, increasing the time period. This makes it easier to measure.
Use expendable springs from a stand and attach masses a little above equilibrium position. Release to start the oscillation. Measure time for 10 oscillations and divide by 10 for time period.
Time is proportional to square root of mass, so drawing a T^2 by m graph gives a linear increasing straight line.

Question 5

What is the formula for maximum velocity?

Answer 5

2pi * frequency * amplitude

Question 6

Consider the model of a baby in a bouncer as an oscillator. When the baby is added into the bouncer, equilibrium position is 0.1m from where the bouncer sat before the baby was added. When the baby is lowered another 0.1 m, how can you find the time period for the baby to reach equilibrium again?

Answer 6

Displacement from equilibrium is 0.1m.
Find angular frequency from using a=-w^2x and using w=2pi*f, rearrange this to obtain f, and so T which is equal to 1/f. Divide T by 4 to obtain time.