Oscillations of a spring and the force constant — NEET & JEE Questions

Question 1 · difficulty L1 · recall

For an ideal spring obeying Hooke's law, what is the restoring force for a displacement $x$ from equilibrium?

• A. $F=-kx$
• B. $F=k/x$
• C. $F=-kx^2$
• D. $F=kx^2$

Question 2 · difficulty L2 · understanding

What is the SI unit of the force constant $k$ of a spring?

• A. N
• B. N m
• C. N/m
• D. J/m

Question 3 · difficulty L2 · understanding

The time period of a mass $m$ attached to an ideal spring of force constant $k$ is

• A. $2\pi\sqrt{\dfrac{m}{k}}$
• B. $2\pi\sqrt{\dfrac{k}{m}}$
• C. $\dfrac{1}{2\pi}\sqrt{\dfrac{m}{k}}$
• D. $2\pi mk$

Question 4 · difficulty L2 · understanding

If the mass attached to an ideal spring is increased while the spring remains unchanged, what happens to the oscillation frequency?

• A. It increases
• B. It decreases
• C. It remains unchanged
• D. It becomes zero for any increase in mass

Question 5 · difficulty L3 · application

A spring extends by $4.0\,\text{cm}$ when a force of $8.0\,\text{N}$ is applied. What is its force constant?

• A. $50\,\text{N m}^{-1}$
• B. $100\,\text{N m}^{-1}$
• C. $200\,\text{N m}^{-1}$
• D. $320\,\text{N m}^{-1}$

Question 6 · difficulty L3 · application

A $1.0\,\text{kg}$ mass is attached to a spring of force constant $100\,\text{N m}^{-1}$. What is the angular frequency of small oscillations?

• A. $5\,\text{rad s}^{-1}$
• B. $10\,\text{rad s}^{-1}$
• C. $20\,\text{rad s}^{-1}$
• D. $100\,\text{rad s}^{-1}$

Question 7 · difficulty L3 · application

A mass-spring oscillator has $m=0.50\,\text{kg}$ and $k=200\,\text{N m}^{-1}$. What is its time period approximately?

• A. $0.10\,\text{s}$
• B. $0.31\,\text{s}$
• C. $0.63\,\text{s}$
• D. $1.57\,\text{s}$

Question 8 · difficulty L3 · application

If the force constant of a spring is made four times its original value while the attached mass is unchanged, how does the time period change?

• A. It becomes $4T$
• B. It becomes $2T$
• C. It becomes $T/2$
• D. It becomes $T/4$

Question 9 · difficulty L4 · application

Two identical springs, each of force constant $k$, are connected in parallel and attached to a mass $m$. What is the time period of small oscillations?

• A. $2\pi\sqrt{\dfrac{m}{2k}}$
• B. $2\pi\sqrt{\dfrac{2m}{k}}$
• C. $2\pi\sqrt{\dfrac{m}{k}}$
• D. $\pi\sqrt{\dfrac{m}{k}}/2$

Question 10 · difficulty L4 · application

Two identical springs, each of force constant $k$, are connected in series and support a mass $m$. What is the ratio of the new time period to the period with only one of the springs?

• A. $1/\sqrt2$
• B. $1$
• C. $\sqrt2$
• D. $2$