Simple harmonic motion/static equilibrium -spring problem, mass given

In summary, the conversation discusses a problem involving a 0.500 kg mass suspended from a spring and set into oscillatory motion. The velocity function is given as Vx(t)=-ωAsin(ωt+\phi). The questions asked are: the period of the motion, the amplitude, the maximum acceleration of the mass, and the force constant of the spring. The attempted solution involves using the equations Vx(t) and Fspring=-k\Deltay, and making assumptions to solve for the unknown variables. However, it is suggested that one more data is needed to solve the problem. A hint is given to determine x(t) and dx/dt as functions of time and use that information to solve for the parameters.
  • #1
mariegrdnr
2
0

Homework Statement



A 0.500 kg mass is suspended from a spring and set into
oscillatory motion. A motion detector is used to record the motion, and it is found that its velocity function is given by Vx(t) What are:
a. the period of the motion;
b. the amplitude;
c. the maximum acceleration of the mass; and
d. the force constant of the spring?

Homework Equations


given
Vx(t)=-ωAsin(ωt+[itex]\phi[/itex])
not given but seems like the way I need to head
Fspring=-k[itex]\Delta[/itex]y
T=2pi[itex]\sqrt{m/k}[/itex]

The Attempt at a Solution


Did FBD where Fspring=-k[itex]\Delta[/itex]y is straight up and weight=4.9N goes straight down. Giving Fnety=
K[itex]\Delta[/itex]L-mg=0
K[itex]\Delta[/itex]L=mg? can I make this assumption or am I missing something?
Also I have three unknowns k,[itex]\Delta[/itex]L, T and can't find another equation to substitute into for third variable. I just need to know if I am heading in the right direction for this problem.
 
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  • #2
To solve the problem, one more data is essential.
 
  • #3
Yes I agree, but none was given, so I was hoping that someone might see something:-(
Thank you for taking a look!
 
  • #4
No, I believe it can be solved with the given info, provided that the mass was set in motion in the usual way by imparting an initial displacement to the system at rest.

Hint: determine x(t) and dx/dt as functions of time. Determine maximum dx/dt. Then determine time t1 at which dx/dt is half of max. This I believe allows solving for every parameter.
 
  • #5


I would first acknowledge the student's attempt at a solution and commend them for their effort. I would then suggest that they review the equations for simple harmonic motion and static equilibrium to ensure they have all the necessary information and equations to solve the problem. It may also be helpful to draw a free body diagram to better understand the forces acting on the mass. Additionally, I would remind the student that the period and amplitude of a simple harmonic motion can be determined from the velocity function, and the force constant of the spring can be calculated using Hooke's Law. I would encourage the student to continue working on the problem and ask for help if they are still having trouble.
 

What is Simple Harmonic Motion?

Simple Harmonic Motion (SHM) is a type of oscillatory motion where the restoring force is directly proportional to the displacement from equilibrium and always acts towards the equilibrium position.

What is Static Equilibrium?

Static equilibrium is a state in which an object is at rest and all forces acting on it are balanced, resulting in no net force and no acceleration.

What is a Spring Problem?

A spring problem is a type of physics problem that involves analyzing the motion and forces of an object attached to a spring. This typically involves applying the principles of SHM and static equilibrium.

How is the Mass of an Object Determined in a Spring Problem?

In a spring problem, the mass of an object is typically given as a known value. However, if it is not given, it can be determined by measuring the object's weight and dividing by the acceleration due to gravity (9.8 m/s^2).

How is the Period of Oscillation Calculated in a Spring Problem?

The period of oscillation (T) in a spring problem can be calculated using the equation T = 2π√(m/k), where m is the mass of the object and k is the spring constant. This equation is derived from the principles of SHM and is applicable for objects oscillating on a spring.

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