A 15-Kg Cart Attached to an Ideal Spring with a Spring

question 31

Short Answer

A 1.5-kg cart attached to an ideal spring with a spring constant of 20 N/m oscillates on a horizontal,frictionless track.At time t = 0.00 s,the cart is released from rest at position x = 10 cm from the equilibrium position.
(a)What is the frequency of the oscillations of the cart?
(b)Determine the maximum speed of the cart.Where does the maximum speed occur?
(c)Find the maximum acceleration of the mass.Where does the maximum acceleration occur?
(d)How much total energy does this oscillating system contain?
(e)Express the displacement as a function of time using a cosine function.

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Definitions:

Variable Production Costs

Expenses that fluctuate in direct proportion to production volume, like labor and materials.

Break-even

The point at which total cost and total revenue are equal, meaning there is no net loss or gain.

Fixed Costs

Expenses that do not change with the level of production or sales, such as rent, salaries, and insurance.

Absorption Costing

An approach in accounting that comprises all costs of manufacturing, like direct materials, direct labor, and both types of manufacturing overheads (variable and fixed), in determining a product's cost.