What's Wrong with My SHM Calculations?

[nonzee]

I've scrolled through other SHO problems and can't really find what I need. I have a homework-test thing and it's only on revision from high school (just started university) and I can't even get it all right!

Q1) A mass m at the end of a spring vibrates with a frequency of 1.06 Hz. When an additional 1.0 kg mass is added to m, the frequency is 0.38 Hz. What is the value of m?

I used the equation f = 1/2pi * (squareroot k/m)

I eventually came up with the answer 1/0.1718 but I've been told this answer is wrong? Can anyone take me through the working out so I know where I was wrong?

Q2) A tuning fork vibrates at a frequency of 237 Hz and the tip of each prong moves 1.93 mm at either side of centre. Calculate the maximum speed of each prong (in m/s).

I thought the formula for this would have been velocity(max) = 2pi*f*A, with 0.000193m as A. I got this formula from my textbook and ended up with 0.29 m/s. However, once again, I was told I was wrong!

Q5) It takes a force of 70 N to compress the spring of a popgun 0.197 m to load a 0.13 kg ball. With what speed will the ball leave the gun?

I'm dumbfounded. Where do I start? F = -kx? v(max) = 2pi*f*A? Somehow I got 10.3966 but i can't understand my own working out (and it's wrong).

Q6) A 0.0127 kg bullet strikes a 0.36 kg block attached to a fixed horizontal spring whose spring constant is 2.62 x103 N/m and sets it into vibration with an amplitude of 12.4 cm.
What was the speed of the bullet?

They failed to mention it, but the bullet actually sticks to the block, too. Anyway I tried to use my good old v(max) = (sqrt(k/m))*A again but my answer, 10.3900, I was informed that it was wrong.

If anyone could help, it'd be fantastic! I really need to know how to do this stuff and my lecturer is always unavailable during my free times.

 

[outandbeyond2004]

You just need to form the ratio first frequency $$f_1$$ to second frequency $$f_2$$ and then solve for m:

$$\frac{f_1}{f_2} = \sqrt{\frac{m + 1}{m}}$$

 

[cookiemonster]

Maybe you should stop looking through your book for formulas that seem to work and should instead start thinking about what each question is asking.

In simple harmonic motion, when is the the velocity greatest? When the forks are fully displaced? When they're not displaced at all? Somewhere inbetween? Once you know the position, how do you calculate the velocity at that position?

When the spring is fully compressed, it has a certain amount of energy stored. When the spring extends, all that stored energy is going to be converted to kinetic energy. So what does this mean for your problem?

Once again, energy! The bullet starts off with some energy that's all transferred to make the block oscillate.

cookiemonster

 

[nonzee]

Thankyou very much for your help
I always did have a weakness for conceptualising but I've finally figured it out.
And sorry for putting it in the wrong place! I'll know next time

 

[HallsofIvy]

Originally posted by cookiemonster:
Maybe you should stop looking through your book for formulas that seem to work and should instead start thinking about what each question is asking.

Cookiemonster- you're starting to sound like me!