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

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