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I am having difficulty answering these theoretical questions. Any help would be greatly appreciated.

In the following physical systems that undergo simple harmonic motion, state which physical quantity or quantities you think will influence the period of motion and in what manner. Briefly justify your predictions using physical arguments rather than equations.

a. mass-spring system (oscillating horizontally on a frictionless surface)

b. simple pendulum

In an ideal mass-spring system (oscillating horizontally on a frictionless surface), the total energy is conserved. What types of energy are involved?

What is the expression for total energy

a. When the mass is at maximum displacement (x = A) in terms of A?

b. When the mass is passing through equilibrium (x = 0) in terms of v_max?

Using the fact that energy is conserved and the expressions found in the previous part, find an expression for maximum speed in terms of m, k and/or A.

Hello Nick,

>In the following physical systems that undergo simple harmonic motion,

>state which physical quantity or quantities you think will influence

>the period of motion and in what manner. Briefly justify your predictions

>using physical arguments rather than equations.

>a. mass-spring system (oscillating horizontally on a frictionless surface)

Greater spring constant, k, will decrease the period. Greater mass, m, will increase the period. In the definition of a simple harmonic oscillator, it is said that the restoring force is proportional to the displacement from the equilibrium position. A higher value of k increases the force. The acceleration increases with increasing force but decreases with increasing m.

>b. simple pendulum

Increasing pendulum rod length increases the period. In a pendulum, for a given displacement from equilibrium, the restoring force is proportional to the elevation gained from the displacement. Longer rods give less elevation for a given displacement, therefore less restoring force. Mass does not change period for the same reason that different mass balls fall at the same rate during free fall. A greater value of g also decreases period -- makes clocks run faster.

>In an ideal mass-spring system (oscillating horizontally on a

>frictionless surface), the total energy is conserved. What types

>of energy are involved?

Kinetic energy and spring potential energy

>What is the expression for total energy

>a. When the mass is at maximum displacement (x = A) in terms of A?

total energy = spring potential energy

>b. When the mass is passing through equilibrium (x = 0) in terms

>of v_max?

total energy = kinetic energy

>Using the fact that energy is conserved and the expressions found

>in the previous part, find an expression for maximum speed in

>terms of m, k and/or A.

max spring potential energy = max kinetic energy

(1/2)*k*A^2 = (1/2)*m*Vmax^2

Vmax^2 = k*A^2 / m

Vmax = A*sqrt(k/m)

I hoep this helps,

Steve

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