1. A 0.500 kg mass is attached to a spring and executes SHM with a velocity given by: v(t) = (3.60cm/s)sin[(4.71rad/s)t − π/2](a) What is the period?(b) What is the amplitude?(c) What is the maximum acceleration of the mass?(d) What is the force constant of the spring?(e) What is the velocity of the mass at t=0?(f) What is the velocity of the mass at t=1.5 s?(g) Write a function for the displacement, x(t), using the fact that at t=0 the mass is at x=0.(h) What is the total energy of the system at t =1.5 s? **1. A 0.500 kg mass is attached to a spring and executes Simple Harmonic Motion (SHM) with a velocity given by:**\[ v(t) = (3.60 \, \text{cm/s}) \sin[(4.71 \, \text{rad/s})t - \pi/2] \]**(a)** What is the period?**(b)** What is the amplitude?**(c)** What is the maximum acceleration of the mass?**(d)** What is the force constant of the spring?**(e)** What is the velocity of the mass at t=0?**(f)** What is the velocity of the mass at t=1.5 s?**(g)** Write a function for the displacement, x(t), using the fact that at t=0 the mass is at x=0.**(h)** What is the total energy of the system at t=1.5 s?

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Description: 1. A 0.500 kg mass is attached to a spring and executes SHM with a velocity given by: v(t) = (3.60cm/s)sin[(4.71rad/s)t − π/2](a) What is the period?(b) What is the amplitude?(c) What is the maximum acceleration of the mass?(d) What is the force

Let us consider the mass of the object attached to a spring is (m) therefore,(m)=0.5 Kg (According to question) This object executes Simple Harmonic Motion with a velocity,v(t) which is function of time given by:- v(t) = (3.60 cm/s) sin[(4.71 rad/sec)t − π/2]----------------------(1) Now, we know object having displacement,x(t) in Simple Harmonic Motion is given by:- x(t)=A cos[ωt-φ]-----------------------------------(2) Now, differentiating above (2) with respect to time we get the velocity of an object in Simple Harmonic Motion as, x'(t)=-A ω sin[ωt-φ]--------------------(3) Now, on comparing (1) & (3) we get, A ω=3.60 cm/sec-----------------------(4) ω=4.71 rad/sec--------------------------(5) &, φ=π/2 rad----------------------------(6)(a.) Let the time period of this Simple Harmonic Motion be (T) in sec. We know, T=2πrad/ω-----------(7) putting values of (ω) from (5) in (7) we get, T=2πrad/4.71 rad/sec T=2π/4.71 sec T=1.33 sec Clearly, the time period of this Simple Harmonic Motion is 1.33 sec respectively. (b.)Let the amplitude of this Simple Harmonic Motion be (A) in cm. Now putting value of (ω) from (5) in (4) we get, A x 4.71 rad/sec =3.60 cm/sec A x 4.71=3.60 cm A=3.60/4.70 cm A=0.76 cm------------(8) Clearly,the amplitude of this Simple Harmonic Motion is 0.76 cm. (c.)Let us consider maximum acceleration of the mass be (amax) in cm/sec2. We know, amax=A x ω2-----------(9) Putting the values of (A) & (ω) from (8) & (5) in (9) we get, amax=0.76 cm x (4.71 rad/sec)2 amax=0.76 x 4.71 x 4.71 cm/sec2 amax=16.85 cm/sec2 Clearly, maximum acceleration of the mass is 16.85 cm/sec2. Note:-As per our guideline we can only solve 3 sub parts of any question. Still if you want other part to be done than send remaining question separately by deleting the previous done parts.Sorry for inconvenience.

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1. A 0.500 kg mass is attached to a spring and executes SHM with a velocity given by: v(t) = (3.60cm/s)sin[(4.71rad/s)t − π/2]

(a) What is the period?
(b) What is the amplitude?
(c) What is the maximum acceleration of the mass?
(d) What is the force constant of the spring?
(e) What is the velocity of the mass at t=0?
(f) What is the velocity of the mass at t=1.5 s?
(g) Write a function for the displacement, x(t), using the fact that at t=0 the mass is at x=0.
(h) What is the total energy of the system at t =1.5 s?

**1. A 0.500 kg mass is attached to a spring and executes Simple Harmonic Motion (SHM) with a velocity given by:**

\[ v(t) = (3.60 \, \text{cm/s}) \sin[(4.71 \, \text{rad/s})t - \pi/2] \]

**(a)** What is the period?

**(b)** What is the amplitude?

**(c)** What is the maximum acceleration of the mass?

**(d)** What is the force constant of the spring?

**(e)** What is the velocity of the mass at t=0?

**(f)** What is the velocity of the mass at t=1.5 s?

**(g)** Write a function for the displacement, x(t), using the fact that at t=0 the mass is at x=0.

**(h)** What is the total energy of the system at t=1.5 s?

Definition Definition Special type of oscillation where the force of restoration is directly proportional to the displacement of the object from its mean or initial position. If an object is in motion such that the acceleration of the object is directly proportional to its displacement (which helps the moving object return to its resting position) then the object is said to undergo a simple harmonic motion. An object undergoing SHM always moves like a wave.

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1. A 0.500 kg mass is attached to a spring and executes SHM with a velocity given by: v(t) = (3.60cm/s)sin[(4.71rad/s)t − π/2] (a) What is the period? (b) What is the amplitude? (c) What is the maximum acceleration of the mass?