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A spring that can be assumed to be ideal hangs from a stand, as shown above. The spring constant, k, of an ideal spring is defined as the force per unit length and differs from one spring to another. It can be measured in both a static (motionless) and dynamic (in motion) mode A You wish to determine experimentally the spring constant k of the spring in a static (motionless) situation What additional, commonly available equipment would you need? ü What measurements would you make? m. How would k be determined from these measurements? 1 B. You wish to determine experimentally the spring constant k of the spring in a dynamic (moving) situation. What additional, commonly available equipment would you need? What measurements would you make C. Assume that the spring constant is determined to be 500 N/m A 20 kg mass is attached to the lower end of the spring and released from rest. Determine the frequency of oscillation of the mass

Respuesta :

(a) The additional commonly available equipment you would need is stop watch.

(b) The measurement obtained with stop watch is period of oscillation. The period of oscillation can be used to determine angular speed and the angular speed is used to determine the spring constant.

(c) The frequency of oscillation of the mass is 0.8 Hz.

Value of spring constant from experiment

The value of spring constant can be determined experimentally with a mass and stop watch to record the period of oscillation.

How to calculate spring constant

k = ω²m

where;

  • ω is angular speed = 2πf = 2π/T
  • m is mass

With a known mass attached to the spring, the period of the oscillation can be determined using stop watch. The period of the oscillation can be used to determine the frequency and angular speed of the oscillation. The angular speed can be used to determine the spring constant, K.

Frequency of the oscillation

ω² = K/m

ω² = 500/20

ω² = 25

ω = √25

ω = 5 rad/s

ω = 2πf

f = ω/2π

f = 5/2π

f = 0.8 Hz

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