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

question 18

Essay

A 1.5-kg cart attached to an ideal spring with a force constant (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:

Protein

Protein is a macromolecule composed of amino acids, essential for the structure, function, and regulation of the body's cells, tissues, and organs.

Pre-mRNA

The primary transcript formed during gene expression in eukaryotes, which undergoes processing to become mature mRNA.

Introns

Non-coding sequences of DNA within a gene that are removed during RNA processing before translation.

Codon

A codon is a sequence of three nucleotides in mRNA that specifies a particular amino acid or start/stop signal for protein synthesis.