heena 3 years ago ques. of SHM

1. heena

five identical springs are used in the following threee configurations. the timeperiod of vertical oscillation in config. a) b) c) are in ratio?? |dw:1328977775731:dw|

2. heena

dont tell the ratio thats the condition ok just tell me how can i solve

3. pruthvi_reddy

K eff for b is K+K/K^2 and for c its just K+K evaluate the rest

4. heena

if x is same means they are arranged in parallel na??

5. heena

thats the trick to find out i guess

6. shankvee\

In a) If you stretch the mass by x then the spring extends by x, hence F=-kx. b) Suppose you stretch by x , the first spring would expand by x1 and the second spring would extend by x2, then x1+x2=x F/k1 + F/k2=F/k. 1/k=1/k1+ 1/k2. c) Again say x is extension then both springs exapnd by x hence F=-k1x-k2x or k=k1+k2.

7. heena

unable to get u as here some springs are attached in paralel ans some are in series rit and i agree wid ur pont den i m not get how u done the b) ??

8. shankvee\

I'll take a general case of b) where the two spring constants are not equal, then if the mass moves by x, obviously both springs move down by some different amounts x1 and x2, but we can say x1+x2=x, as the net extension is still x. and x1=F/k1. This would be series. c) is parallel.

9. amitlpu91

|dw:1328372813777:dw|

10. amitlpu91

so now total exerting force by all this spring & then find out the ratio

11. heena