Question

A 323 g object is attached to a spring and executes simple harmonic motion with a period of 0.210 s. If the total energy of the system is 6.70 J.

(a) Find the maximum speed of the object.
m/s

(b) Find the force constant of the spring.
N/m

(c) Find the amplitude of the motion.
mA 323 g object is attached to a spring and executes simple harmonic motion with a period of 0.210 s. If the total energy of the system is 6.70 J.

(a) Find the maximum speed of the object.
m/s

(b) Find the force constant of the spring.
N/m

(c) Find the amplitude of the motion.
m

Answer 1

total energy of the system E = 6.70 J

                     ( 1/ 2) m V ² = 6.70J

where m = mass = 323 g = 0.323 kg

maximum speed of the object V = ?[ (2 * 6.70) / m]

                                                = 3.66 m / s

(b).  force constant of the spring K = m ?²

where ? = angular frequency = 2? / T

           T= time period = 0.210 s

So, ? = 29.91 rad / s

? K = 288.95 N / m

(c). Amplitude of motion A = V / ?

                                          = 0.1223 m