How do I solve this LTI acceleration sensor problem?

In summary, the conversation is about a homework problem involving a system's impulse response and input signal. The output is represented by the convolution of the two, while the Laplace transform turns it into the product of the transfer function and input signal in the frequency domain. The conversation also touches on questions about units and the use of Laplace transform to move signals to the frequency domain. The problem is ultimately solved using the formula X(s) = a0/s.
  • #1
Nikitin
735
27

Homework Statement


Please see he attached file for the problem text.

Homework Equations


The output ##y(t) = h(t) * x(t)##, where ##h(t)## is the system's impulse response while ##x(t)## is the input signal.

Laplace transformed, the formula above turns into ## Y(s)=H(s) \cdot X(s)##, where ##H(s)## is the transfer function.

The Attempt at a Solution



Uhm, well.. I am very lost.

1) Why does the transfer function have units Volt/Acceleration ? Isn't it the impulse response that should have those units?

2) Why exactly does a laplace-transform of a signal move the signal to the frequency domain? Is it just because the new variable has units 1/Second ?

Anyway, to solve this problem I know that ##X(s)=a_0/s##, since ##x(t) = a_0 u(t)##, with ##u(t)## being the unit-step function. But how do I proceed?
 

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  • #2
Guys the problem is solved. no need to answer
 

Related to How do I solve this LTI acceleration sensor problem?

1. What is an LTI Acceleration sensor?

An LTI (linear time invariant) Acceleration sensor is a device that measures the acceleration of an object. It is commonly used in scientific experiments and engineering applications to track movement and changes in velocity.

2. How does an LTI Acceleration sensor work?

An LTI Acceleration sensor works by using a transducer to convert mechanical motion into an electrical signal. This signal is then amplified and processed to calculate the acceleration of the object being measured.

3. What are some common uses of LTI Acceleration sensors?

LTI Acceleration sensors are commonly used in industries such as automotive, aerospace, and robotics to monitor and improve performance. They are also used in research and development to study the movement and behavior of various objects.

4. What are the advantages of using LTI Acceleration sensors?

One of the main advantages of using LTI Acceleration sensors is their high accuracy and precision in measuring acceleration. They are also compact, durable, and have a fast response time, making them suitable for a wide range of applications.

5. How do I choose the right LTI Acceleration sensor for my project?

When choosing an LTI Acceleration sensor, it is important to consider factors such as the measurement range, sensitivity, and frequency response. It is also important to ensure that the sensor is compatible with the data acquisition system or software being used for data analysis.

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