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Q. No.

Two springs of spring constants \(k_1\) and \(k_2\) are joined in series. The effective spring constant of the combination is given by:
1. \(\frac{k_1+k_2}{2}\)
2. \(k_1+k_2\)
3. \(\frac{k_1k_2}{k_1+k_2}\)
4. \(\sqrt{k_1k_2}{}\)

Subtopic:  Combination of Springs |
 94%
Level 1: 80%+
AIPMT - 2004
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If two identical springs, each with a spring constant \(k,\) are connected in series, the new spring constant and time period will change by a factor of:

1. \( \dfrac{1}{2},~ \sqrt{2} \) 2. \( \dfrac{1}{4},~ \sqrt{2} \)
3. \( \dfrac{1}{4},~ 2 \sqrt{2} \) 4. \( \dfrac{1}{2},~ 2 \sqrt{2} \)
Subtopic:  Combination of Springs |
 88%
Level 1: 80%+
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Two identical springs of spring constant \(k\) are attached to a block of mass \(m\) and to fixed supports as shown in the figure. When the mass is displaced from its equilibrium position on either side, it executes a simple harmonic motion. The period of oscillations is:

      

1. \(2 \pi \sqrt{\dfrac{{m}}{4{k}}}\)
2. \(2 \pi \sqrt{\dfrac{2{m}}{{k}}}\)
3. \(2 \pi \sqrt{\dfrac{{m}}{2{k}}}\)
4. \(2 \pi \sqrt{\dfrac{{m}}{{k}}}\)
Subtopic:  Combination of Springs |
 85%
Level 1: 80%+
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A spring having a spring constant of \(1200\) N/m is mounted on a horizontal table as shown in the figure. A mass of \(3\) kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of \(2.0\) cm and released. The maximum acceleration of the mass is:

1. \(6\) ms–2 2. \(8\) ms–2
3. \(3.3\) ms–2 4. \(5.1\) ms–2
Subtopic:  Combination of Springs |
 85%
Level 1: 80%+
Hints

What is the period of oscillation of the block shown in the figure?

1. \(2\pi \sqrt{\dfrac{M}{k}}\) 2. \(2\pi \sqrt{\dfrac{4M}{k}}\)
3. \(\pi \sqrt{\dfrac{M}{k}}\) 4. \(2\pi \sqrt{\dfrac{M}{2k}}\)
Subtopic:  Combination of Springs |
 85%
Level 1: 80%+
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As per the given figures, two springs of spring constants \(k\) and \(2k\) are connected to mass \(m.\) If the period of oscillation in figure \((a)\) is \(3~\text s,\) then the period of oscillation in figure \((b)\) is \(\sqrt x ~\text s.\) The value of \(x \) is:
       
1. \(3\)
2. \(4\)
3. \(2\)
4. \(1\)
Subtopic:  Combination of Springs |
 81%
Level 1: 80%+
JEE
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A body mass m is attached to the lower end of a spring whose upper end is fixed. The spring has neglible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5s. The value of m in kg is-

1. 34               

2. 43

3. 169               

4. 916

Subtopic:  Combination of Springs |
 80%
Level 1: 80%+
NEET - 2016
Hints
Infinite springs with force constants \(k,\) \(2k,\) \(4k,\) \(8k,....\) respectively are connected in series. The effective force constant of the spring will be:
1. \(20k\)
2. \(40k\)
3. \(k/2\)
4. none of these
Subtopic:  Combination of Springs |
 80%
Level 1: 80%+
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If two identical springs of stiffness \(k\) (each) are combined end-to-end, the resulting spring has a stiffness:
1. \(k\)
2. \(2k\)
3. \(\dfrac k2\)
4. zero
Subtopic:  Combination of Springs |
 79%
Level 2: 60%+
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The period of oscillation of the system shown below is:
 
1. \(\pi \sqrt{\dfrac{4 m}{5 k}}\) 2. \(\pi \sqrt{\dfrac{6 m}{5 k}}\)
3. \(\pi \sqrt{\dfrac{12m}{5 k}}\) 4. \(\pi \sqrt{\dfrac{8m}{5 k}}\)
Subtopic:  Combination of Springs |
 79%
Level 2: 60%+
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