Solving for Spring Constant: Displacement and Time Relationship

In summary, the conversation discussed finding the spring constant for a small mass attached to a spring, given the displacement versus time graph and the mass of the object. The equation for displacement as a function of time was also derived using the given information.
  • #1
Holly3.9
2
0

Homework Statement



The graph of displacement versus time for a small mass at the end of a spring is shown. At t = 0, x = 0.43 cm. (a) If m = 14.3 g, find the spring constant, k. (b) Write the equation for displacement x as a function of time.

Homework Equations



f = (1/2pi) * SQRT (k/m)
f = 1/Period = 1/ 0.69 sec = 1.45 cycles/sec
SQRT (k/m) = 2 * pi * f

k = m * (2 * pi * f )^2

k = 0.0143 kg * (2 * pi * 1.45 cycles/sec
)^2


The Attempt at a Solution



1.19 N/m
 
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  • #2
graph : http://www.webassign.net/userimages/mowat@ncsu/FG14_029.JPG

SORRY!
 
  • #3
Your k value is correct.
The general equation of oscillation is
x = x0*sin(ωt + φ)
When t = 0, x = x0*sin(φ)
Put the values of the x and xo and find the value of φ. Then write the general equation.
 

1. What is an oscillation problem?

An oscillation problem is a type of physics problem that involves the movement or varying state of an object or system in a repeated back-and-forth motion around a fixed point or equilibrium. This can also be referred to as a vibration or harmonic motion.

2. What are some common examples of oscillation problems?

Some common examples of oscillation problems include a pendulum swinging back and forth, a spring bouncing up and down, and a guitar string vibrating when plucked. Other examples can include the motion of a mass on a spring, a swinging amusement park ride, or the movement of a simple harmonic oscillator.

3. How are oscillation problems solved?

Oscillation problems are typically solved using mathematical equations that describe the motion of the object or system. These equations can involve parameters such as mass, length, frequency, and amplitude. The solution to the problem can then be found by applying these equations and solving for the unknown variables.

4. What is the role of oscillation problems in science?

Oscillation problems are important in science because they help us understand the behavior and properties of systems in motion. They are used in various fields such as mechanics, acoustics, and optics to study the effects of oscillations on different objects and materials. They also have practical applications in fields such as engineering, where understanding and controlling oscillations is crucial.

5. What are some real-world implications of oscillation problems?

Oscillation problems have many real-world implications, especially in the fields of engineering and technology. They are used to design structures and machines that can withstand and utilize oscillations, such as bridges, buildings, and musical instruments. Oscillation problems also play a role in the development of technologies such as clocks, radios, and ultrasound machines.

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