Sriman Dutta Posted October 7, 2017 Share Posted October 7, 2017 Hi, I'm back after a lot of days...... Just came back with a thought... Suppose there is a block of mass m that has compressed a light ideal spring having spring constant k. Now, if we write the equation of motion for this system, then ma=-kx or a=-kx/m It's evident that a is a function of x. So we can differentiate it wrt x to gt the jerk j. So, j=-kv/m. But v is variable and still differentiable. And continuing it, we have an endless chain. So is it infinitely differentiable?? Link to comment Share on other sites More sharing options...
mathematic Posted October 7, 2017 Share Posted October 7, 2017 Your development has x as a function of something, so that you get x'=v. In order to answer your question you need an explicit statement of the dependence of x or v on the something (time?). Link to comment Share on other sites More sharing options...
Sriman Dutta Posted October 8, 2017 Author Share Posted October 8, 2017 x isn't a function of any variable. It's the position vector of the block from the mean position. Link to comment Share on other sites More sharing options...
Country Boy Posted October 8, 2017 Share Posted October 8, 2017 If f is not a function of any variable, then it makes no sense to talk about its derivative. If this is a "deterministic problem', which it would be if you are using Newtonian physics as in you first post, x will have a specific value for any specific time. In that case, x is a function of the time. Perhaps you are not clear on what the word "function" means. 1 Link to comment Share on other sites More sharing options...
Dubbelosix Posted October 10, 2017 Share Posted October 10, 2017 If you are though, don't be ashamed to admit it, I am sure Ivy doesn't mean to cause offence. Link to comment Share on other sites More sharing options...
Sriman Dutta Posted October 15, 2017 Author Share Posted October 15, 2017 If I consider x=Asin(wt) ?? Link to comment Share on other sites More sharing options...
John Cuthber Posted October 15, 2017 Share Posted October 15, 2017 If you have something whose position varies sinusoidally with time then the acceleration is a cosine curve and the derivative of that is a sine function so you are back to where you started. You can keep differentiating as often as you like- the functions are all well behaved. There's a similar situation with an object moving in a circle. The acceleration is always towards the centre of the circle and the rate of change of the acceleration is circular too. You can differentiate as much as you want. Link to comment Share on other sites More sharing options...
Country Boy Posted October 18, 2017 Share Posted October 18, 2017 On 10/15/2017 at 8:18 AM, Sriman Dutta said: If I consider x=Asin(wt) ?? So x is a function of t. v= dx/dt= Aw cos(wt) and a= dv/dt= -Aw^2 sin(wt)= -w^2 x. In your original post you had a=-kx/m so w^2= k/m. Link to comment Share on other sites More sharing options...
Sriman Dutta Posted October 19, 2017 Author Share Posted October 19, 2017 Thank you for all the help. Link to comment Share on other sites More sharing options...
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