Question

A 400 gram mass is attached to a horizontal spring with a frequency of 2 Hz. The mass has a speed of 40 cm/s and is located at x=5 cm..

A) find the period of motion

B) find the amplitude of motion

C) find the maximum speed of the mass

D) find the total energy of the mass

Answer 1

(A) Period of motion -

T = 1 / f = 1 / (2.0) = 0.50 s

(B) ? = 2?f

? = 2?( 2 Hz )
? = 12.57 rad / sec

Now -

Max potential = kinetic + potential
½kA² = ½kx² + ½mv²
kA² = kx² + mv²
A² = x² + mv² / k
A² = x² + mv² / m?²
A² = x² + ( v/? )²
A² = ( 5 cm )² + ( 40 cm/s / 12.57 s?¹ )²
A² = 35.13 cm²
A = 5.93 cm

So, amplitude of motion = 5.93 cm

(C) Max speed = A?
= ( 5.93 cm )( 12.57 s?¹ )
= 74.54 cm/s

(D) Total energy = max kinetic energy
= ½m( max speed )²
= ½ ( 0.40 kg )( 74.54 cm/s )²
= 1111 kg cm²/s²
= 0.1111 Joules