Question

A 3.95 kg mass attached to a spring oscillates with a period of 0.365 s and an amplitude of 19.0 cm.

(a) Find the total mechanical energy of the system.

(b) Find the maximum speed of the mass.

Answer 1

(a) 21.11 J

(b) 3.3 m/s

Step-by-step explanation:

(a)

m = mass attached to the spring = 3.95 kg

A = amplitude of the oscillation = 19 cm = 0.19 m

T = Time period of oscillation = 0.365 s

U = Total mechanical energy

Total mechanical energy is given as

`U = (0.5)mA^(2)\left ( (2\pi )/(T) \right )^(2)`

`U = (0.5)(3.95)(0.19)^(2)\left ( (2(3.14) )/(0.365) \right )^(2)`

U = 21.11 J

(b)

v = maximum speed of the mass

maximum speed of the mass is given as

`v = A\left ( (2\pi )/(T) \right )`

`v = (0.19)\left ( (2(3.14) )/(0.365) \right )`

`v` = 3.3 m/s