Answer :
The speed is 3.41 m/s.
The spring is attached to a mass. This is also the Simple Harmonic Motion. The SHM is the motion that is made in a straight line periodically and the acceleration is 'always' in a same direction.
Given,
Mass = 92.7g = 0.0927kg
A = 38.8cm = 0.388m
K = 9.59N/m
At equilibrium position, there's total conservation of energy.
Total energy = kinetic energy + potential energy
Total Energy = K.E + P.E
½KA² = ½mv² + ½kx²
½KA² = ½(mv² + kx²)
KA² = mv² + kx²
Collect like terms
KA² - Kx² = mv²
K(A² - x²) = mv²
V² = k/m (A² - x²)
V = √(K/m (A² - x²) )
note x = ½A
V = √(k/m (A² - (½A)²)
V = √(k/m (A² - A²/4))
Resolve the fraction between A.
V = √(¾. K/m. A² )
V = √(¾ * (9.59/0.0927)*(0.388)²)
V = √(0.75 * 103.45 * 0.150)
V = √(11.68)
V = 3.41 m/s
Hence, the speed of the mass when it is halfway to the equilibrium position if the surface is frictionless is 3.41 m/s.
To know more about SHM, refer: https://brainly.com/question/26549854
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