Simple Harmonic Motion of bobble toy

In summary, the problem involves finding the spring constant and mass of a bobble head doll based on its oscillation frequency and observed spring stretch in equilibrium. The equation T = 2pi square root(m/k) can be used, but since the mass and spring constant are not given, we must use the information that the spring stretches 2 cm under a force mg to determine their relationship.
  • #1
Jennisa
1
0
*note: my previous thread will be deleted because I didn't include relevant equations + I put two unrelated problems in the same thread.

1. Homework Statement

A cat bobble head doll consists of a weighted head on top of a spring. When the head hangs straight sown in equilibrium, it is observed that the spring stretches 2cm. When the head is displaced upward by 1 cm, it is observed to oscillate with a frequency of 3 Hz.

a) Find the spring constant of the bobble head
b) Find the mass of the bobble head

Homework Equations



T = 2pi square root (m/k)

The Attempt at a Solution



I tried to use the formula T = 2pi square root(m/k) to find m and k but I cannot use this because the mass and k are not given.
 
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  • #2
No, but you know that the spring stretches 2 cm under a force mg. What does that tell you about the relationship between k and m ?
 

What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which the restoring force acting on an object is directly proportional to the displacement of the object from its equilibrium position. This means that as the object moves away from its equilibrium position, there is a force pulling it back towards it, creating a back-and-forth motion.

What is a bobble toy?

A bobble toy, also known as a bobblehead or nodder, is a type of novelty toy that has a head attached to a body by a spring or hinge. When the base is tapped or moved, the head bounces and wobbles in a characteristic back-and-forth motion.

What factors affect the frequency of a bobble toy's motion?

The frequency of a bobble toy's motion is affected by the stiffness of the spring or hinge, the mass of the head, and the gravitational acceleration of the object. A stiffer spring or hinge, a heavier head, and a higher gravitational acceleration will result in a higher frequency of motion.

How does the amplitude of a bobble toy's motion affect its period?

The amplitude, or maximum displacement, of a bobble toy's motion does not affect its period. The period, or time it takes for one complete cycle of motion, is only dependent on the factors mentioned above (stiffness, mass, and gravitational acceleration).

What real-life applications use simple harmonic motion of bobble toys?

Simple harmonic motion of bobble toys is often used as a demonstration of the principles of physics, particularly in the field of oscillations and waves. It can also be seen in various amusement park rides, such as the "Wacky Worm" roller coaster, which mimics the back-and-forth motion of a bobble toy.

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