# What is the spring constant of the spring?

A block with mass m =7.1 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.23 m. While at this equilibrium position, the mass is then given an initial push downward at v = 4.5 m/s. The block oscillates on the spring without friction.

1)What is the spring constant of the spring? I got this correct as 302.83 using (mg)/(x)
2)What is the oscillation frequency? I got this correct as 1.039 using w^2= k/m
3) After t = 0.37 s what is the speed of the block? I got this correct using v=-wacos(wt) answer was 4.496
4) What is the magnitude of the maximum acceleration of the block? I got this one wrong attempt posted below.

so I took the derivative of function in question 3 and got a= w^(2)asin(wt) now I then plugged in wa from question 3, but I was not sure what to plug in for the other w so I plugged in the w I got from problem two into the sin argument and the other w in w^(2)a. I then got .197011 m/s^(2) as my answer which is wrong. what do I need to do to correct this error? thank you for the assistance

## Answers and Replies

What is the magnitude of the maximum acceleration of the block? I got this one wrong attempt posted below.

so I took the derivative of function in question 3 and got a= w^(2)asin(wt) now I then plugged in wa from question 3, but I was not sure what to plug in for the other w so I plugged in the w I got from problem two into the sin argument and the other w in w^(2)a. I then got .197011 m/s^(2) as my answer which is wrong. what do I need to do to correct this error? thank you for the assistance

when the block will have maximum acceleration -when it will have the maximum force acting on it .
so if you draw a free body diagram of the block in oscillation ,when it is having the experience of maximum force-
the spring force is proportional to the extension or compression so at maximum value of amplitude it should have maximum acceleration .
perhaps you have information of amplitude!

when the block will have maximum acceleration -when it will have the maximum force acting on it .
so if you draw a free body diagram of the block in oscillation ,when it is having the experience of maximum force-
the spring force is proportional to the extension or compression so at maximum value of amplitude it should have maximum acceleration .
perhaps you have information of amplitude!

Thank you for the help

haruspex
Science Advisor
Homework Helper
Gold Member
2020 Award
I plugged in the w I got from problem two into the sin argument
But there is also a t in the sine argument. What will be the maximum value of sin(ωt) as t varies?

Tom.G
Science Advisor
Lets try a different approach.

1) Is this a harmonic oscillator?
2) In what manner does its position vary with time?
3) As the block travels from its rest position, what happens to its speed?
4) What is the waveform of its speed?

Lets try a different approach.

1) Is this a harmonic oscillator?
2) In what manner does its position vary with time?
3) As the block travels from its rest position, what happens to its speed?
4) What is the waveform of its speed?

1. i think it is a harmonic oscillator under spring force
2. its position , velocity, acceleration varies as a harmonic oscillator, the speed will also have the the same waveform with max. at he mean position and zero at the extreme end.
moreover maximum acceleration will not occur at max. speed point of displacement as
harmonic force- leading to harmonic osc. is spring force F = - k. displacement

haruspex
Science Advisor
Homework Helper
Gold Member
2020 Award
1. i think it is a harmonic oscillator under spring force
2. its position , velocity, acceleration varies as a harmonic oscillator, the speed will also have the the same waveform with max. at he mean position and zero at the extreme end.
moreover maximum acceleration will not occur at max. speed point of displacement as
harmonic force- leading to harmonic osc. is spring force F = - k. displacement
I would assume Tom G's questions were directed to derphysiker09.

Tom.G
I would assume Tom G's questions were directed to derphysiker09.

extremely sorry ;
somehow i felt he is raising the basic framework of HO formalism and focusing on the speed .

Tom.G
haruspex
Science Advisor
Homework Helper
Gold Member
2020 Award
extremely sorry ;
somehow i felt he is raising the basic framework of HO formalism and focusing on the speed .
Not your fault. Whenever there is potential for confusion over whom the post is directed towards the Reply button or other quoting should be used.

Tom.G
Science Advisor
I would assume Tom G's questions were directed to derphysiker09.
Yes, they were. Sorry about the confusion!