Question

A 261 g object attached to a horizontal spring moves in simple harmonic motion with a period of 0.240 s. The total mechanical energy of the spring-mass system is 6.46 J. (a) What is the maximum speed of the object (in m/s)

Answer 1

Answer:maximum speed of the object =7.0 m/s

Step-by-step explanation:

The total energy of the system is, given as

E = 1/2mω²A ²

but ωA=
`\sqrt{2E/m`------ equation 1

Also. Linear speed is given as

v = ωA …… equation 2

From equation 1 and 2 ,

v=
`\sqrt2E/m`

Total energy = 6.46J

mass = 261g to kg becomes 261/1000= 0.261kg

v=
`\sqrt2E/m`

v=
`\sqrt2 x 6.46/0.261\\`

v=
`\sqrt 12.92J/0.261Kg`

v=
`\sqrt 49.50`

v=7.0 m/s