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The time period and the amplitude of an object executing simple harmonic motion, under the restoring force of a spring, are 3.14 seconds and 0.2 m, respectively. If the mass of the object is 2 kg, the maximum force (in Newton) exerted by the spring on the object is
  • a)
    1.6
  • b)
    3.2 
  • c)
    4.6
  • d)
    5.2 
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The time period and the amplitude of an object executing simple harmon...
Given:
- Time period (T) = 3.14 seconds
- Amplitude (A) = 0.2 m
- Mass of the object (m) = 2 kg

Formula:
The time period (T) of an object executing simple harmonic motion can be calculated using the formula:
T = 2π√(m/k)
where k is the spring constant.

The angular frequency (ω) of the object can be calculated using the formula:
ω = 2π/T

The maximum force (Fmax) exerted by the spring on the object can be calculated using the formula:
Fmax = kA

Calculation:
Given that T = 3.14 seconds, we can calculate ω as follows:
ω = 2π/T = 2π/3.14 ≈ 2 radians/second

To find the spring constant (k), we need to calculate ω^2:
ω^2 = (2 radians/second)^2 = 4 radians^2/second^2

Now, we can calculate the spring constant (k):
k = mω^2 = 2 kg * 4 radians^2/second^2 = 8 kg radians^2/second^2

Using the formula for the maximum force (Fmax), we can calculate:
Fmax = kA = 8 kg radians^2/second^2 * 0.2 m = 1.6 N

Therefore, the maximum force exerted by the spring on the object is 1.6 Newtons (Option A).
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The time period and the amplitude of an object executing simple harmonic motion, under the restoring force of a spring, are 3.14 seconds and 0.2 m, respectively. If the mass of the object is 2 kg, the maximum force (in Newton) exerted by the spring on the object isa)1.6b)3.2c)4.6d)5.2Correct answer is option 'A'. Can you explain this answer?
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The time period and the amplitude of an object executing simple harmonic motion, under the restoring force of a spring, are 3.14 seconds and 0.2 m, respectively. If the mass of the object is 2 kg, the maximum force (in Newton) exerted by the spring on the object isa)1.6b)3.2c)4.6d)5.2Correct answer is option 'A'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about The time period and the amplitude of an object executing simple harmonic motion, under the restoring force of a spring, are 3.14 seconds and 0.2 m, respectively. If the mass of the object is 2 kg, the maximum force (in Newton) exerted by the spring on the object isa)1.6b)3.2c)4.6d)5.2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The time period and the amplitude of an object executing simple harmonic motion, under the restoring force of a spring, are 3.14 seconds and 0.2 m, respectively. If the mass of the object is 2 kg, the maximum force (in Newton) exerted by the spring on the object isa)1.6b)3.2c)4.6d)5.2Correct answer is option 'A'. Can you explain this answer?.
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