Spring Mass Systems

Question 1

Multiple choice general knowledge science & technology

What is the natural frequency of mass m having stiffness k

k/m
m/k
sq root of (m/k)

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Answer

sq root of (k/m)

Question 2

Multiple choice

The spring balance works on the principle of

Boyle's law
Bernouli's theorem
Pascal's law

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Answer

Hooke's law

Question 3

Multiple choice

Choose the correct option

Mass is measured with a spring balance and weight is measured with a pan balance.
Both the mass and weight are measured with a spring balance.
Both the mass and weight are measured with a pan balance.
Both 1 and 2.

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Answer

Mass is measured with a pan balance and weight is measured with a spring balance.

Question 4

Multiple choice

An acceleration has a seismic mass of 0.06 kg and a spring constant of 4500 N/m. Maximum mass displacement is + - 0.025 m (before mass hits the top). Determine maximum measurable acceleration and natural frequency.

1275 m/s; 60 Hz
1875 Hz; 44 m/s
4113 m/s; 60 Hz

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Answer

1875 m/s; 44 Hz

Question 5

Multiple choice

Directions: A rigid beam is hinged at one end and supported on linear elastic springs (both having a stiffness of ‘k’) at points ‘1’ and ‘2’, and an inclined load acts at ‘2’, as shown.

If the load P equals 100 kN, which of the following options represents forces R₁ and R₂ in the springs at points ‘1’ and ‘2’?

R₁ = 20 kN and R₂ = 40 kN
R₁ = 50 kN and R₂ = 50 kN
R₁ = 30 kN and R₂ = 60 kN

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Answer

R₁= 40 kN and R₂ = 8O kN

Question 6

Multiple choice

Considering a massless rigid rod and small oscillations. The natural frequency (in rad/s) of vibration of the system, as shown in the figure, is

$\sqrt{\frac{400}{1}}$
$\sqrt{\frac{400}{2}}$
$\sqrt{\frac{400}{3}}$

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Answer

$\sqrt{\frac{400}{4}}$

Question 7

Multiple choice

Directions: Carry Two Marks Each.

The given figure shows a single degree of freedom system. The system consists of a massless rigid bar OP hinged at O and a mass m at end P. The natural frequency of vibration of the system is

^{$f_n=\frac{1}{2\pi}\sqrt{\frac{k}{4\pi}}$}
$f_n=\frac{1}{2\pi}\sqrt{\frac{k}{m}}$
^{$f_n=\frac{1}{2\pi}\sqrt{\frac{2k}{m}}$}

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Answer

^{$f_n=\frac{1}{2\pi}\sqrt{\frac{k}{4m}}$}

Question 8

Multiple choice

What is the natural frequency of the spring mass system shown below? The contact between the block and the inclined plane is frictionless. The mass of the block is denoted by m and the spring constants are denoted by k₁ and k₂ as shown below.

$\sqrt{\frac{k_1 + k_2}{2m}}$
$\sqrt{\frac{k_1 + k_2}{4m}}$
$\sqrt{\frac{k_1 - k_2}{m}}$

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Answer

$\sqrt{\frac{k_1 + k_2}{m}}$

Question 9

Multiple choice

A concentrated mass m is attached at the centre of a rod of length 2L as shown in the figure. The rod is kept in a horizontal equilibrium position by a spring of stiffness k. For very small amplitude of vibration, neglecting the weights of the rod and spring, the undamped natural frequency of the system is

$\sqrt{\frac{k}{m}}$
$\sqrt{\frac{2k}{m}}$
$\sqrt{\frac{k}{2m}}$

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Answer

$\sqrt{\frac{4k}{m}}$

Question 10

Multiple choice

A rigid uniform rod AB of length L and mass m is hinged at C such that AC = L/3, CB = 2L/3. Ends A and B are supported by springs of spring constant k. The natural frequency of the system is given by

$\sqrt\frac{k}{2m}$
$\sqrt\frac{k}{m}$
$\sqrt\frac{2k}{m}$

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Answer

$\sqrt\frac{5k}{m}$

Question 11

Multiple choice

A mass of 1 kg is attached to two identical springs each with stiffness k = 20 kN/m as shown in the figure. Under frictionless condition, the natural frequency of the system in Hz is close to

32
23
16
11

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Answer

0.471 and 1.19 Hz

Question 12

Multiple choice

A vehicle suspension system consists of a spring and a damper. The stiffness of the spring is 3.6 kN/m and the damping constant of the damper is 400 Ns/m. If the mass is 50 kg, the damping factor(d) and damped natural frequency (f_n), respectively, are

0.471 and 7.48 Hz
0.666 and 1.35 Hz
0.666 and 8.50 Hz

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Question 13

Multiple choice

An automotive engine weighing 240 kg is supported on four springs with linear characteristics. Each of the front two springs have a stiffness of 16 MN/m while the stiffness of each rear spring is 32 MN/m. The engine speed (in rpm), at which resonance is likely to occur, is

6040
3020
1424
955

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Question 14

Multiple choice

A cantilever type gate hinged at Q is shown in the figure. P and R are the centers of gravity of the cantilever part and the counter weight respectively. The mass of the cantilever part is 75 kg. The mass of the counter weight, for static balance is

75 kg
150 kg
225 kg
300 kg

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Question 15

Multiple choice

A uniform rigid rod of mass m = 1 kg and length L = 1 m is hinged at its centre and laterally supported at one end by a spring of spring constant k = 300 N/m. The natural frequency $\omega_n$ in rad/s is

10
20
30
40

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Spring Mass Systems

Spring Mass Systems Questions