Find the time period of the oscillation of mass m in figures-xyzi 2 - m - k 1- k 2ii 2 -mk1-k2-k1 k2iii 2 -mk1-k2-k1 k2A- x - ii- y - i- z - iiiB- x - i- y - i- z - iiC- x - i- y - ii- z - iiD- x - i- y - iii- z - ii

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Springs in Parallel and Series

Find the time...

Question

Find the time period of the oscillation of mass m in figures.

(i) $2 π \sqrt{\frac{m}{k_{1} + k_{2}}}$

(ii) $2 π \sqrt{\frac{m (k_{1} + k_{2})}{k_{1} k_{2}}}$

(iii) $2 π \sqrt{\frac{m (k_{1} - k_{2})}{k_{1} k_{2}}}$

(x) - (i); (y) - (ii); (z) - (ii)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(x) - (i); (y) - (i); (z) - (ii)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

(x) - (ii); (y) - (i); (z) - (iii)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(x) - (i); (y) - (iii); (z) - (ii)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
(x) - (i); (y) - (i); (z) - (ii)

a) Equivalent spring constant $k = k_{1} + k_{2}$ (parallel)

$T = 2 π \sqrt{\frac{M}{k}} = 2 π \sqrt{\frac{m}{k_{1} + k_{2}}}$

b) Let us, displace the block m towards left through displacement `x'

Resultant force $F = F_{1} + F_{2} = (k_{1} + k_{2}) x$

Acceleration $(F / m) = \frac{(k_{1} + k_{2}) x}{m}$

Time period $T = 2 π \sqrt{\frac{d i s p l a c e m e n t}{A c c e l e r a t i o n}} = 2 π \sqrt{\frac{\frac{x}{x (k_{1} + k_{2})}}{m}} = 2 π \sqrt{\frac{m}{k_{1} + k_{2}}}$

The equivalent spring constant $k = k_{1} + k_{2}$

c) In series combination, let equivalent spring constant be k.

So, $\frac{1}{k} = \frac{1}{k_{1}} + \frac{1}{k_{2}} = \frac{k_{2} + k_{1}}{k_{1} k_{2}} \Rightarrow k = \frac{k_{1} k_{2}}{k_{1} + k_{2}}$

$T = 2 π \sqrt{\frac{M}{k}} = 2 π \sqrt{\frac{m (k_{1} + k_{2})}{k_{1} k_{2}}}$

Suggest Corrections

Similar questions

Find the time period of the oscillation of mass m in figures.

(i) $2 π \sqrt{\frac{m}{k_{1} + k_{2}}}$

(ii) $2 π \sqrt{\frac{m (k_{1} + k_{2})}{k_{1} k_{2}}}$

(iii) $2 π \sqrt{\frac{m (k_{1} - k_{2})}{k_{1} k_{2}}}$

Q. Two springs of force constants

k_{1}

and

k_{2}

are connected as shown figure. The time period of vertical oscillations of mass m is given by

A projectile is fired horizontally from a gun that is 45.0 m above flat ground, it emerges from the gun with a speed of 500 m/s. (take, g = $- 10 m / s^{2}$ )

$C o l u m n - I C o l u m n - I I$
$(i) T i m e o f f l i g h t o f P r o j e c t i l e i n s (x) 3$
$(i i) H o r i z o n t a l d i s t a n c e c o v e r e d b y p r o j e c t i l e i n m (y) 30$
$(i i i) M a g n i t u d e o f v e r t i c a l c o m p o n e n t o f v e l o c i t y (z) 1500$
$i n m / s a s i t s t r i k e s g r o u n d$

Q. Let

x, y, z

be positive reals. Which of the following implies

x = y = z ?

(I)

x^{3} + y^{3} + z^{3} = 3 x y z

(II)

x^{3} + y^{2} z + y z^{2} = 3 x y z

(II)

x^{3} + y^{2} z + z^{2} x = 3 x y z

(II)

(x + y + z)^{3} = 27 x y z

How will the resistance be affected if the various parameters are changed as follows?
$\begin{matrix} i) Length increases & x) Resistance increases ii) Area increases & y) Resistance decreases iii) Resistivity decreases & z) Resistance remains the same iv) Temperature increases v) Velocity increases \end{matrix}$

Join BYJU'S Learning Program

Find the time period of the oscillation of mass m in figures. (i) 2π√mk1+k2 (ii) 2π√m(k1+k2)k1k2 (iii) 2π√m(k1−k2)k1k2

Find the time period of the oscillation of mass m in figures.

(i) $2 π \sqrt{\frac{m}{k_{1} + k_{2}}}$

(ii) $2 π \sqrt{\frac{m (k_{1} + k_{2})}{k_{1} k_{2}}}$

(iii) $2 π \sqrt{\frac{m (k_{1} - k_{2})}{k_{1} k_{2}}}$